85 Sentences With "forms a group" | Random Sentence Generator

He forms a group of vigilantes called the Phantom Thieves, which steal the treasures of corrupted adults in the Metaverse in order to rehabilitate the adults through a change of heart.

The set of all such matrices of size n forms a group, known as the special orthogonal group .

Whichever village wins the match gets to have the market square, and the other village is driven out. To make matters worse, to test whether Seema Raja is just severely infatuated or genuinely in love with her and ascertain if he is a good suitor, Selvi tells Seema Raja to lose the wrestling match. Seema Raja is devastated. Seema Raja forms a group of other not serious fighters, whilst Puliyampatti forms a group of very built fighters.

The parish of Aldermaston forms a group with the local parishes of Wasing and Brimpton. The three share a monthly Parish Magazine featuring stories from churches, organisations, schools, businesses and various miscellany.

Proguithera is a genus of thread-legged bug in the Emesinae. This genus forms a group with two other genera, Guithera and Lutevula. The relationship between the group is unclear at the moment.

The set of translations and rotations together form the rigid motions or rigid displacements. This set forms a group under composition, the group of rigid motions, a subgroup of the full group of Euclidean isometries.

"Mëniku & Campos 2012, p. 2. "Albanian is an Indo- European language, but like modern Greek and Armenian, it does not have any other closely related living language. Within the Indo-European family, it forms a group of its own. In Albanian, the language is called shqip.

The church forms a group of buildings with the Hall. Dedicated to St Mary it dates largely from the 13th century but has had many perpendicular features added. The south porch was added in 1635. It was restored in 1865 to designs by architects Goddard & Son and again in 1878.

The mountain underwent partial collapse just before the Anyuyskiy volcano formed. The volcano together with Aluchin and Bilibin forms a group of volcanoes which were active in the late Pleistocene era. Volcanic activity at Anyuyskiy probably began with lava flows. These three lava flows have a total volume of and cover .

Broseley's amateur dramatics society, BroADS, puts on several plays a year. Every month, the Birchmeadow Centre is used by Broseley Cinema, to show well-rated films on its own large screen. There is a thriving arts and crafts community that forms a group known as the Broseley Artists.Shropshire Council Retrieved 31 October 2017.

Eventually, after a particularly bad incident concerning children that she babysits, she takes the initiative to leave the oppressive cult and forms a group of her own of "Seekers", those hollowed from their experiences in Fishers. Her faith in God remains strong, and she considers herself to be searching for the truth.

The composition of two automorphisms is another automorphism, and the set of automorphisms of a given graph, under the composition operation, forms a group, the automorphism group of the graph. In the opposite direction, by Frucht's theorem, all groups can be represented as the automorphism group of a connected graph – indeed, of a cubic graph...

David R. Lide (Hrsg.): CRC Handbook of Chemistry and Physics. 90. Auflage. (Internet-Version: 2010), CRC Press/Taylor and Francis, Boca Raton, Florida, Physical Constants of Organic Compounds, S. 3-136. The average molar mass is 138.25 g/mol. 5-Decyne forms a group of symmetric alkynes with 4-octyne, 3-hexyne, and 2-butyne.

The Kleiner Deister, Nesselberg and Osterwald The Nesselberg is a ridge up to high in the Calenberg Highland which, together with the Kleiner Deister and the Osterwald, forms a group of three contiguous hill regions in the northwestern part of the Leine Uplands. It lies between Altenhagen I and Coppenbrügge in Lower Saxony, Germany.

The temple was therefore assigned the Azure Dragon, guardian of the East and one of the Four Symbols. The temple's honorific mountain name, , was meant to signify that every wish was fulfilled at Saimyō-ji. Together with Kongōrin-ji in Aishō and Hyakusai-ji in Higashiōmi the temple forms a group of three temples known as .

Heydour is a hamlet and civil parish in the South Kesteven district of Lincolnshire, England. The parish population of 286 at the 2001 census rose to 311 at the 2011 census. Heydour lies about south-west of Sleaford and north- east of Grantham. It forms a group of parish hamlets with Kelby, Culverthorpe, Oasby and Aisby.

Kleiner Deister, Nesselberg and Osterwald The Kleiner Deister is a ridge of hills (up to ) in the Calenberg Uplands which, together with the Nesselberg and the Osterwald, forms a group of three adjacent hill ranges in the northern part of the Leine Uplands. It lies between Springe and Eldagsen in Hanover region in Lower Saxony, Germany.

Southport Arts Centre was designated as a Grade II listed building on 15 November 1972. Grade II is the lowest of the three grades of listing and is applied to buildings that are "nationally important and of special interest". The arts centre forms a group with other Grade II listed buildings nearby, the Atkinson Art Gallery and Library, and the Town Hall.

In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.

The Canary Wharf complex within Docklands on the Isle of Dogs forms a group of some of the tallest buildings in Europe. One Canada Square was the first to be constructed and is the second tallest in London. Nearby are the HSBC Tower, Citigroup Centres and One Churchill Place, headquarters of Barclays Bank. Within the same complex are the Heron Quays offices.

At 16 he moves to France for secondary schooling. Fascinated by the silver screen he enters the artistic scene by joining the "Théatre de l’Atelier", directed by Jean Darnel. As he learns the ropes and forms a group of aficionados, he eventually directs his first short film, "l’enfer". Satisfied by the results the group of actors joined him for his second short film, "le tourbillon".

In abstract algebra, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.

In 1997 he forms a group Stil and the same year publishes the retrospective album "Stvaranje" featuring 21 of his songs written in the period between 1988 and 1997 In 2004 he publishes the album "Jutro". Antolić also works together with the singer Željka Marinović as a composer and songwriter. Her album "Želim ti dati najbolje" won a Porin for spiritual music in 2001.

There is a Church of England parish church and a Methodist church in the village. The Church of St Edward dates from the early 13th century, with alterations in the 15th, 16th, 18th and late 19th centuries. There are a number of interesting brass and stone monuments inside. The building forms a group with the Manor House and the Rectory, which are also listed.

The Lavedan (in gascon eth/lo Lavedan, /et/lu laβedã/), or occasionally vallées des Gaves, denotes a mountainous natural region of France, located at the heart of the Pyrénées, and forms a group of valleys upstream of Lourdes. The Lavedan is historically part of the Gascony province and of the county of Bigorre. Today, it is situated in the Hautes-Pyrénées department in the Midi- Pyrénées region.

Antofalla is a Miocene-Pliocene volcano in Argentina's Catamarca Province. It is part of the volcanic segment of the Andes in Argentina, and it is considered to be part of the Central Volcanic Zone, one of the volcanic zones of the Andes. Antofalla forms a group of volcanoes that are aligned on and behind the main volcanic arc. Antofalla itself is a remote volcano.

The church is still an active parish church within the local community. The former parishes of St Mary's and St Michael’s were joined to form a single parish with St Michael’s as the parish church and St Mary’s designated as a Chapel of Ease. Together with St John’s at Wall it forms a group of churches known as the United Benefice. Regular services take place on Sundays, Tuesdays and Wednesdays.

Consider a topological space, that is, a space with some notion of closeness between points in the space. We can consider the set of homeomorphisms from the space into itself, that is, continuous maps with continuous inverses: functions which stretch and deform the space continuously without breaking or glueing the space. This set of homeomorphisms can be thought of as a space itself. It forms a group under functional composition.

Given a geometry, the set of motions forms a group under composition of mappings. This group of motions is noted for its properties. For example, the Euclidean group is noted for the normal subgroup of translations. In the plane, a direct Euclidean motion is either a translation or a rotation, while in space every direct Euclidean motion may be expressed as a screw displacement according to Chasles' theorem.

CS Camelopardalis (CS Cam) is a binary star in reflection nebula VdB 14, in the constellation Camelopardalis. It forms a group of stars known as the Camelopardalis R1 association, part of the Cam OB1 association. The near- identical supergiant CE Camelopardalis is located half a degree to the south. The primary component, CS Camelopardalis A, is a blue-white B-type supergiant with a mean apparent magnitude of 4.21m.

The set of all invertible elements in a monoid M, together with the operation •, forms a group. In that sense, every monoid contains a group (possibly only the trivial group consisting of only the identity). However, not every monoid sits inside a group. For instance, it is perfectly possible to have a monoid in which two elements a and b exist such that holds even though b is not the identity element.

The set of all translations of the plane with composition as operation forms a group: #If a and b are translations, then a ∘ b is also a translation. #Composition of translations is associative: (a ∘ b) ∘ c = a ∘ (b ∘ c). #The identity element for this group is the translation with prescription "move zero miles in whatever direction you like". #The inverse of a translation is given by walking in the opposite direction for the same distance.

The game is set in an alternate 1975, Sid Burn and his band of Coyotes are hired by OMAR to dispose of all competing oil companies in the U.S. so that they can become the richest company in America. After hearing reports of destruction by the Coyotes, a man named Convoy, a kind-hearted trucker, forms a group of his own, the Vigilantes, to combat the Coyotes and to stop the tyranny of OMAR.

Its closest relatives appear to be the chestnut-naped antpitta and the pale- billed antpitta, with which it forms a group of antpittas with uniform breast plumage and smoky-grey flanks. This bird's specific name honors the ornithologist Robert S. Ridgely, who took part in the initial discovery of this species. The common name refers to the local name of the bird, jocotoco, which is onomatopoetic after its hooting calls and song.

In mathematics, a Borel isomorphism is a measurable bijective function between two measurable standard Borel spaces. By Souslin's theorem in standard Borel spaces (a set that is both analytic and coanalytic is necessarily Borel), the inverse of any such measurable bijective function is also measurable. Borel isomorphisms are closed under composition and under taking of inverses. The set of Borel isomorphisms from a space to itself clearly forms a group under composition.

More specifically, they can be characterized as orthogonal matrices with determinant 1; that is, a square matrix is a rotation matrix if and only if and . The set of all orthogonal matrices of size with determinant +1 forms a group known as the special orthogonal group , one example of which is the rotation group SO(3). The set of all orthogonal matrices of size with determinant +1 or −1 forms the (general) orthogonal group .

One of the most common group-item strategies is row-column scanning in which each row forms a group. The rows of items are scanned and when a row is selected, the items in the row are scanned one at a time until a message is selected. There are three main selection control techniques in scanning. In "automatic scanning", the scan proceeds at a pre-determined speed and pattern until the user selects an item.

Yakushi Nyorai surrounded by the Twelve Heavenly Generals The 191.5 cm, Heian period seated Yakushi Nyorai is the principal image of Shin-Yakushi-ji. He is placed on a huge (9 m diameter, 90 cm high) circular platform (Dais) which almost entirely fills the Hon-dō. Together with six small on its halo, the main statue forms a group of . Yakushi Nyorai is protected by Twelve Heavenly Generals arranged in a circular fashion around it facing outward.

An automorphism, A, of the octonions is an invertible linear transformation of O which satisfies :A(xy) = A(x)A(y). The set of all automorphisms of O forms a group called G2. The group G2 is a simply connected, compact, real Lie group of dimension 14. This group is the smallest of the exceptional Lie groups and is isomorphic to the subgroup of Spin(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation.

A police station in Bow Street is mentioned in the Sherlock Holmes story The Man with the Twisted Lip. At the station, Holmes reveals that the beggar Hugh Boone is the aristocrat Neville St. Clair in disguise. Bow Street is one of the streets on the British version of the game Monopoly, which is based in London. It forms a group with Marlborough Street and Vine Street, all of which have connections to the police and law.

Lozada and her brand strategist, Courtney Parker, wrote the 2012 novel The Wives Association: Inner Circle. Released by Cash Money Content books, the novel follows a young woman who marries a football star and then forms a group of other sports wives - The Wives Association. In 2019, Lozada published the novel, The Perfect Date which was co-written with Holly Lorincz. In 2020, Lozada is scheduled to publish another novel co-written with Holly Lorincz entitled The Wrong Mr. Darcy.

Among the significant memorials in the church are a monument, built in 1910 by Albert Toft and dedicated to Alistair Mackenzie, and an art nouveau-style wall tablet. Outside are the village stocks and Abinger Common War Memorial, with which the church forms a group of listed buildings. The war memorial was designed by Sir Edwin Lutyens, who also designed the nearby house Goddards; it was damaged by the same V-1 flying bomb as the church, and was restored in 1948.

G/N has identity element N and the inverse of element aN can always be represented by a−1N. Therefore, the set G/N together with the operation defined by (aN)(bN) = (ab)N forms a group, the quotient group of G by N. Due to the normality of N, the left cosets and right cosets of N in G are the same, and so, G/N could have been defined to be the set of right cosets of N in G.

The town hall was designated as a Grade II listed building on 15 November 1972. Grade II is the lowest of the three grades of listing and is applied to buildings that are "nationally important and of special interest". The authors of the Buildings of England series comment that the design is "quite modest ... but impressive". The town hall forms a group with other Grade II listed buildings nearby, the Atkinson Art Gallery and Library, and the Southport Arts Centre.

Aruba ( , , ) is an island and a constituent country of the Kingdom of the Netherlands lying in the southern Caribbean Sea, located about north of the Venezuelan peninsula of Paraguaná and northwest of Curaçao. It measures long from its northwestern to its southeastern end and across at its widest point. Together with Bonaire and Curaçao, Aruba forms a group referred to as the ABC islands. Collectively, Aruba and the other Dutch islands in the Caribbean are often called the Dutch Caribbean.

A fundamental result in group theory, Cayley's theorem, essentially says that any group is in fact just a subgroup of a permutation group (up to isomorphism). The set of all bijective functions (called permutations) forms a group with respect to function composition. This is the symmetric group, also sometimes called the composition group. In the symmetric semigroup (of all transformations) one also finds a weaker, non-unique notion of inverse (called a pseudoinverse) because the symmetric semigroup is a regular semigroup.

Another way to create a dynamical system is to define an odometer. Informally, this is exactly what it sounds like: just "add one" to the first position, and let the odometer "roll over" by using carry bits as the odometer rolls over. This is nothing more than base-two addition on the set of infinite strings. Since addition forms a group (mathematics), and the Bernoulli process was already given a topology, above, this provides a simple example of a topological group.

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below under classification of Euclidean plane isometries). The set of Euclidean plane isometries forms a group under composition: the Euclidean group in two dimensions. It is generated by reflections in lines, and every element of the Euclidean group is the composite of at most three distinct reflections.

Planet Express faces foreclosure and to raise money, Professor Farnsworth, Fry, Bender, Zoidberg, Hermes and Scruffy take advantage of a contract clause to force Leela, Amy, and LaBarbara to pose for a pin-up calendar. This plan does not work out, so the company converts into a private airline. During its maiden voyage the plane runs out of fuel and crashes on a planet made entirely of minerals with rivers of mercury. Tensions begin to arise between the males and females, and each gender forms a group.

Jettu had died in the accident and is now a ghost, too. Massu forms a group of loitering ghosts to earn money by performing fake exorcisms and extorting money from scared, rich people, while promising the ghosts that he would fulfill their last wishes in return. Meanwhile, Manini, who thought Massu was working in a finance company, gets to know about the fake exorcisms and leaves him in a heist. One day, Massu meets a ghost called Shakthivel, a Sri Lankan Tamil and lookalike of Massu.

Like almost every Berberis species in South-America, B. empetrifolia belongs to the subgenus Australes, characterised by simple, evergreen leaves and glaucous, purplish to black berries. Within that subgenus, B. empetrifolia forms a group with B. actinacantha, B. congestiflora, B. rotundifolia, B. horrida, B. microphylla, B. glomerata, B. grevilleana, and B. comberi. This group more or less shares the following character states: leafy spines, flowers in umbels, short styles, filaments with teeth, and palmately veined leaves. Berberis empetrifolia occurs to form natural hybrids with at least B. grevilleana and B. montana.

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation. The group of all symmetries is isomorphic to the group S4, the symmetric group of permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating subgroup A4 of S4.

Both of the buildings are recorded in the National Heritage List for England as designated Grade II listed buildings. The original Atkinson Art Gallery and Library building was designated on 15 November 1972, and the former bank was designated on 29 July 1999. Grade II is the lowest of the three grades of listing and is applied to buildings that are "nationally important and of special interest". The Atkinson Art Gallery and Library forms a group with other Grade II listed buildings nearby, Southport Town Hall and the Southport Arts Centre.

Icosahedral symmetry fundamental domains soccer ball, a common example of a spherical truncated icosahedron, has full icosahedral symmetry. A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation. A regular dodecahedron has the same set of symmetries, since it is the dual of the icosahedron. The set of orientation-preserving symmetries forms a group referred to as A5 (the alternating group on 5 letters), and the full symmetry group (including reflections) is the product A5 × Z2.

Berberis ilicifolia was first described by Georg Forster in 1789. B. lagenaria described by Jean Louis Marie Poiret in 1808, and B. subarctica described by Michel Gandoger in 1913 both are now regarded as synonyms of B. ilicifolia. Like almost every Berberis species in South-America, B. ilicifolia belongs to the subgenus Australes, characterised by simple, evergreen leaves and glaucous, purplish to black berries. Within that subgenus, B. ilicifolia forms a group with B. chilensis, B. litoralis, B. valdiviana, B. darwinii, B. trigona, B. serratodentata, B. negeriana, and probably B. laurina.

Vampire War (also called the Hunters trilogy) is the third trilogy in The Saga of Darren Shan by Darren Shan. It contains the novels Hunters of the Dusk, Allies of the Night and Killers of the Dawn. This trilogy continues the war between vampires and vampaneze. Mr Tiny forms a group of three "hunters" - Darren Shan, Mr Crepsley and new character Vancha March, a Vampire Prince who lives in the wild and follows the old vampire traditions, and has unusually pink skin from staying out in the sun too long.

Sde Eliyahu 1946 Sde Eliyahu 1947 Sde Eliyahu was founded on 8 May 1939 by Jewish refugees from Nazi Germany as a tower and stockade settlement. It was named after the 19th-century Rabbi Eliyahu Guttmacher, one of the early leaders of Religious Zionism, and together with Ein HaNatziv, Shluhot and Tirat Zvi forms a group of religious kibbutzim in the area. After the 1948 Arab–Israeli War, Sde Eliyahu have used the land of the depopulated Palestinian village of Arab al-'Arida. Immigrants from many other countries have since joined Sde Eliyahu.

This Roberts Mill may have been owned by either William Roberts (abt 1738-bef 1810) or his father John Roberts (abt 1703-abt 1802). The Laurel Mills store Laurel Mills has a cohesive collection of mid-to-late-19th-century architectural resources associated with the Rappahannock Woolen Mills. The structures in the village represent the Greek Revival, Queen Anne, Italianate and Gothic Revival architectural forms. A group of three workers' houses dating to approximately 1840 features several common -story wood-framed houses with stone foundations, while the impressive mill ruins of the Rappahannock Woolen Mills Company represent early 20th- century industrial architecture.

Sabancaya, with Ampato in the background Sabancaya is high and rises above the surrounding terrain. It forms a group of volcanoes with the northern Hualca Hualca and the southern Ampato in the Cordillera Occidental, which tower above the Colca Canyon in the north and the Siguas Valley in the southwest. Ampato and the more heavily eroded Hualca Hualca are the dominant volcanoes of this group, with Sabancaya forming a northeastward extension of the former away from Ampato's summit. There is evidence of age progression from the oldest, Hualca Hualca, over Ampato, to the youngest volcano, Sabancaya.

When Stryfe travels to the present, Cable follows him with the aim of stopping Stryfe's plans as well as preventing Apocalypse's rise to power. Cable forms a group initially called the Wild Pack, but conflict with Silver Sable (who already had a group called the Wild Pack) forces him to change the name to the Six Pack. Cable travels between the present and his future with his ship Graymalkin, which contained a sentient computer program called Professor (the future version of the program built into X-Factor's Ship). The Six Pack performs many brutal missions, often with a high body count.

It is claimed in the National Trust survey of ocean and harbour pools that Wylie's Baths is the oldest surviving communal sea baths in Australia. Wylie's Baths is also historically significant in the development of amateur swimming clubs in Sydney and the development of competitive swimming in Australia. It forms a group with a number of other early Olympic-sized harbour and ocean swimming pools in Sydney built between the 1880s and the First World War to cater to the popularity of competitive swimming. This group of early pools predate the main construction phase of ocean pools in the 1930s and 1940s.

The former Bank of New South Wales building is a two-storeyed stuccoed masonry structure on the corner of Flinders Street East and Wickham Street, Townsville. With the Tattersalls Hotel, the Queensland Building and the Burns Philp Building, it forms a group of late-19th century commercial buildings on the four corners of this intersection. Flinders Street East also retains many other late-19th century commercial masonry buildings. The principle facades of the Bank of NSW building are set on the street alignments of Flinders and Wickham Streets, and joined by a curved bay at the street corner.

The group of bijective linear transformations of the plane to itself (real matrices with non-zero determinant) naturally induces bijections of the space of lines in the plane to itself, which form a group of self-homeomorphisms of the space of lines. Hence the same group forms a group of self-homeomorphisms of the Möbius band described in the previous paragraph. But there is no metric on the space of lines in the plane that is invariant under the action of this group of homeomorphisms. In this sense, the space of lines in the plane has no natural metric on it.

The simplest such group is U(1), which appears in the modern formulation of quantum electrodynamics (QED) via its use of complex numbers. QED is generally regarded as the first, and simplest, physical gauge theory. The set of possible gauge transformations of the entire configuration of a given gauge theory also forms a group, the gauge group of the theory. An element of the gauge group can be parameterized by a smoothly varying function from the points of spacetime to the (finite- dimensional) Lie group, such that the value of the function and its derivatives at each point represents the action of the gauge transformation on the fiber over that point.

The historic population was found to possess twice the genetic diversity of modern wolves, which suggests that the mDNA diversity of the wolves eradicated from the western U.S. was more than twice that of the modern population. Some haplotypes possessed by the Mexican wolf, the extinct Great Plains wolf, and the extinct Southern Rocky Mountain wolf were found to form a unique "southern clade". All North American wolves group together with those from Eurasia, except for the southern clade which forms a group that is exclusive to North America. The wide distribution area of the southern clade indicates that gene flow was extensive across the recognized limits of its subspecies.

The high quality of its construction and detailing is unusual for rental housing of this type and is evidence of the standards set by Edward Stanley Ebsworth who commissioned its construction c.1881. Despite some alterations, including those to the interior and exterior of the rear extension, it remains a good example of Victorian terrace housing in The Rocks, sharing similar characteristics and qualities to this type of housing in east Sydney. Avery Terrace forms a group with Playfair and Argyle Terrace which are of a similar style and scale. The group retains many intact architectural elements, and survives as evidence of a late 19th century streetscape in The Rocks.

The episode begins with Michael Stone's release from prison. Tricking Ash, Stacie and Albert into believing that he is to carry out one last con before he retires, Mickey forms a group to perform an investment scam on a businessman, Peter Williams, telling him to invest with brilliant returns. Danny, having not impressed Mickey earlier in the episode, turns up at a key moment in the con to convince Williams to take part, gaining him entry to the group. However, Danny is approached by police officers who tell him to testify to shorten the trial, and in a confrontation with Mickey, Mickey is shot in the head.

Jenny managed to defeat Vladmir and his army (with her head attached to Tuck's r/c race car) by luring them into the swimming pool where the rats' natural instincts forced them to "abandon ship" (Jenny's body). Wakeman kept Vladimir for further experiments while his comrades were taken away by Pest Control. Apparently his mutated look is a reference Disney's "Mickey Mouse". Vladimir returns in the season three episode "The Legion of Evil" where he forms a group of Jenny's old foes—Lancer, the Mudslinger, and the Mad Hammer Brothers—to exact their revenge on Jenny and steal a priceless Egyptian pillow made entirely of diamond.

The Chronicon Ambrosianum () or Chronica parva Ambrosianum ("short Ambrosian chronicle") is a set of exceedingly terse Latin annals that, together with the Annales Compostellani and the Chronicon Burgense, forms a group of related histories first called the Efemérides riojanas by Manuel Gómez-Moreno because they may have been compiled in La Rioja. The Chronicon is named after the Biblioteca Ambrosiana in Milan, where the Chronicon was first discovered in manuscript and published by Ludovico Antonio Muratori. The Chronicon contains a list of ten feast days with the names of their saints and seventeen years, each described by one event. The first event, in Era 38, is the nativity of Jesus.

The place is important in demonstrating aesthetic characteristics and/or a high degree of creative or technical achievement in New South Wales. A remarkably fine set of Edwardian baroque sandstone elevations forming a complete city block and providing a landmark building to Bridge Street where it forms a group with the Lands Department and Chief Secretary's Office and the older portions of the Intercontinental hotel (the former Treasury). The fine external character and detailing is also found in several vestibules and several major interiors. The place has a strong or special association with a particular community or cultural group in New South Wales for social, cultural or spiritual reasons.

Between occasional sips from his mug, he strums a lute and sings: > The song I sing Will tell the tale : of a cold and wintery day; Of castle > walls And torchlit halls : And a price men had to pay. When evil fled And > brave men bled : The Dark one came to stay, 'Til men of old For blood and > gold : Had rescued Skara Brae. In the actual game, the player forms a group of up to six characters. Game progress is made through advancing the characters so that they are powerful enough to defeat the increasingly dangerous foes and monsters in the dungeons, obtaining certain items relevant to solving the overall quest, and obtaining information.

The free group with two generators a and b consists of all finite strings that can be formed from the four symbols a, a−1, b and b−1 such that no a appears directly next to an a−1 and no b appears directly next to a b−1. Two such strings can be concatenated and converted into a string of this type by repeatedly replacing the "forbidden" substrings with the empty string. For instance: "abab−1a−1" concatenated with "abab−1a" yields "abab−1a−1abab−1a", which gets reduced to "abaab−1a". One can check that the set of those strings with this operation forms a group with neutral element the empty string ε := "".

For every positive integer n, the set of the integers modulo n that are relatively prime to n is written as (Z/nZ)×; it forms a group under the operation of multiplication. This group is not always cyclic, but is so whenever n is 1, 2, 4, a power of an odd prime, or twice a power of an odd prime ... This is the multiplicative group of units of the ring Z/nZ; there are φ(n) of them, where again φ is the Euler totient function. For example, (Z/6Z)× = {1,5}, and since 6 is twice an odd prime this is a cyclic group. In contrast, (Z/8Z)× = {1,3,5,7} is a Klein 4-group and is not cyclic.

The Permotanyderidaea are an extinct family of insects within the order Protodiptera. Along with Permotipulidae (Permotipula and Permila, Willmann, 1989) and the Robinjohniidae (Robinjohnia, Scherbakov ET to., 1995), the somewhat more distantly related Permotanyderidae forms a group of mecopteroids of the Late Permian of Australia and Eurasia (250-260 Ma) that represents the older close relatives of the true flies. The first two genera had separate wings (presumably the front), while the last two have been created from complete specimens: The Robinjohniidae had four wings of about the same size, while the hind wings of the Choristotanyderus nanus (Permotanyderidae) specimens had a size of about half of the front, and the mesothorax was great.

The set C of such Cauchy sequences forms a group (for the componentwise product), and the set C_0 of null sequences (s.th. \forall r, \exists N, \forall n > N, x_n \in H_r) is a normal subgroup of C. The factor group C/C_0 is called the completion of G with respect to H. One can then show that this completion is isomorphic to the inverse limit of the sequence (G/H_r). An example of this construction, familiar in number theory and algebraic geometry is the construction of the p-adic completion of the integers with respect to a prime p. In this case, G is the integers under addition, and Hr is the additive subgroup consisting of integer multiples of pr.

Those who wished to overtly oppose the Nazis in their art either worked abroad (for example, André Masson) or clandestinely, as part of the resistance movement (such as André Fougeron). In the public space, resistance took on more symbolic forms. A group known as 'Jeunes peintres de tradition française' exhibited in Paris for the first time in 1941. The works they produced during the period were characterised by semi-abstract art and bright colours, which they considered as a form of resistance to the Nazis.Lionel Richard, L’art et la guerre: Les artistes confrontés à la Seconde guerre mondiale, Paris, Flammarion, 1995, p. 190 Other supposedly non-political works were ambiguous – they observed the hardships of life in France without apportioning blame.

At a farewell ceremony in Krasnoyarsk, a band of young Soviet Army recruits is preparing to leave for military duty. Lyutyi (Artur Smolyaninov) one of the conscripts forms a group along with Chugun (Ivan Kokorin), Gioconda (Konstantin Kryukov), Ryaba (Mikhail Evlanov), Stas (Artyom Mikhalkov), Seryi (Ivan Nikolaev), and Vorobey (Aleksey Chadov). They have different talents and personalities that made it hard for them to form a bond with each other at first. On arrival at their bootcamp in the Fergana Valley of Uzbekistan, they meet another recruit, Pinochet (Soslan Fidarov), a Chechen recruit from Grozny, and their drill instructor, Senior Praporschik Dygalo, a seasoned, traumatized veteran of several tours in Afghanistan and a brutal trainer who treats the recruits harshly.

In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group. The group is so named because the columns of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position. To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix.

The book tells us the story of Demetrio Macías, a peasant who, after having a misunderstanding with a local cacique (land owner), is hunted by the government soldiers (Federales) and decides to flee when they arrive at his home and kill his dog Palomo (dove), prompting him to abandon his family and take revenge. He escapes to the mountains and forms a group of rebels who support the Mexican Revolution. The whole novel has various reading levels and the character names represent forces or ideals beyond the characters themselves. Some of them are prototypes of the kind of people that were dragged into the revolution, like Demetrio, whose name is associated with the goddess of farming and agriculture Demeter; the dog, Palomo, killed at the beginning who symbolizes peace.

In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a set G is any bijective function taking G onto G. The set of all permutations of G forms a group under function composition, called the symmetric group on G, and written as Sym(G). Cayley's theorem puts all groups on the same footing, by considering any group (including infinite groups such as (R,+)) as a permutation group of some underlying set. Thus, theorems that are true for subgroups of permutation groups are true for groups in general. Nevertheless, Alperin and Bell note that "in general the fact that finite groups are imbedded in symmetric groups has not influenced the methods used to study finite groups".

The place is important in demonstrating the course, or pattern, of cultural or natural history in New South Wales. It is thought that the location for Wylie's Baths may be, or may be near a place that was special to Aboriginal women's business, possibly associated with birthing, although more research needs to be done to confirm this. Wylie's Baths survives as one example of the numerous seaside attractions built at Coogee Beach around the turn of the twentieth century to attract visitors and day-trippers, with other attractions including an aquarium, pier, shark net, floodlighting etc. The construction of Wylie's Baths in 1907 coincided with an emerging interest in seaside baths in Sydney. Wylie's Baths forms a group with the three other ocean pools at Coogee Beach which date from the late nineteenth and early twentieth centuries: McIver Women's Baths (built 1886); Giles, former men's only (built 1902); and the Ross Jones Memorial Pool (built 1947).

The Desargues graph is a symmetric graph: it has symmetries that take any vertex to any other vertex and any edge to any other edge. Its symmetry group has order 240, and is isomorphic to the product of a symmetric group on 5 points with a group of order 2\. One can interpret this product representation of the symmetry group in terms of the constructions of the Desargues graph: the symmetric group on five points is the symmetry group of the Desargues configuration, and the order-2 subgroup swaps the roles of the vertices that represent points of the Desargues configuration and the vertices that represent lines. Alternatively, in terms of the bipartite Kneser graph, the symmetric group on five points acts separately on the two-element and three-element subsets of the five points, and complementation of subsets forms a group of order two that transforms one type of subset into the other.

A linear transformation f: V → V is an endomorphism of V; the set of all such endomorphisms End(V) together with addition, composition and scalar multiplication as defined above forms an associative algebra with identity element over the field K (and in particular a ring). The multiplicative identity element of this algebra is the identity map id: V → V. An endomorphism of V that is also an isomorphism is called an automorphism of V. The composition of two automorphisms is again an automorphism, and the set of all automorphisms of V forms a group, the automorphism group of V which is denoted by Aut(V) or GL(V). Since the automorphisms are precisely those endomorphisms which possess inverses under composition, Aut(V) is the group of units in the ring End(V). If V has finite dimension n, then End(V) is isomorphic to the associative algebra of all n × n matrices with entries in K. The automorphism group of V is isomorphic to the general linear group GL(n, K) of all n × n invertible matrices with entries in K.

In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K contains H strictly. In other words, H is a maximal element of the partially ordered set of proper subgroups of G. Maximal subgroups are of interest because of their direct connection with primitive permutation representations of G. They are also much studied for the purposes of finite group theory: see for example Frattini subgroup, the intersection of the maximal subgroups. In semigroup theory, a maximal subgroup of a semigroup S is a subgroup (that is, a subsemigroup which forms a group under the semigroup operation) of S which is not properly contained in another subgroup of S. Notice that, here, there is no requirement that a maximal subgroup be proper, so if S is in fact a group then its unique maximal subgroup (as a semigroup) is S itself.

The Methodist Church in Marlborough Square is a good example of design by the local architect, Thomas Ignatius McCarthy, and together with the art deco cinema houses and former Lloyds bank forms a group of characterful buildings, though their impact is possibly detracted by the use of the square as a public car park. The Methodist Church, built as a Primitive Methodist chapel in 1903, contains a gallery extending around the interior, accessed by two polygonal towers either side of a large, four-light lancet widow on the frontal facade. The Miners' Memorial Statue is a bronze sculpture situated on the site of the old railway station and which was officially unveiled by David Taylor MP and the Right Reverend William Down, Assistant Bishop of Leicester, in 1998 to mark the one hundredth anniversary of the Whitwick Colliery Disaster, in which thirty five men and boys lost their lives. The inscription reads: "This memorial is dedicated to all miners of Leicestershire who gave their lives winning the coal".