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- | image = ATLAS of Finite Groups cover.jpg | caption = ''ATLAS of Finite Groups'' distinctive cherry red cardboard cover and spiral binding ...7 KB (1,012 words) - 08:15, 18 February 2025
- ...[[discrete Fourier transform]] from [[cyclic group|cyclic]] to arbitrary [[finite group]]s. ...' of a function <math>f : G \to \Complex</math> at a [[representation of a finite group|representation]] <math>\varrho : G \to \mathrm{GL}_{d_\varrho}(\Compl ...12 KB (1,939 words) - 16:27, 25 February 2025
- ...on of certain highly symmetric [[Group action (mathematics)|actions]] of [[finite group]]s on [[vector space]]s. ...vides a complete <!-- and irredundant? --> list of the finite 2-transitive groups whose socle is [[elementary abelian group|elementary abelian]]. ...7 KB (962 words) - 20:45, 9 February 2024
Page text matches
- ...s]], the '''B-theorem''' is a result in [[Group theory#Finite group theory|finite group theory]] formerly known as the '''B-conjecture'''. ...k|last1=Gorenstein|first1=Daniel|title=The Classification of finite simple groups|date=1983|publisher=Plenum Press|location=New York|isbn=978-0-306-41305-6|p ...762 bytes (109 words) - 04:54, 16 August 2024
- ...fined over a [[finite field]], the higher [[algebraic K-theory|algebraic K-groups]] vanish up to torsion:<ref>Conjecture 51 in {{cite book|title=Handbook of ==Finite fields== ...2 KB (287 words) - 05:50, 22 June 2022
- ...theory)|order]] relatively prime to ''p'' and a [[p-group|''p''-group]]. A finite group is an elementary group if it is ''p''-elementary for some [[prime num [[Brauer's theorem on induced characters]] states that a character on a finite group is a linear combination with integer coefficients of characters [[ind ...2 KB (226 words) - 13:16, 13 August 2023
- ...'''' (where ''X'' is some property of groups) if it "can be recovered from groups with property ''X''". * [[Residually finite group|Residually finite]] ...1 KB (169 words) - 17:49, 26 April 2017
- In [[finite group|finite]] [[group theory]], a branch of [[mathematics]], a group is said to be of ' ...cteristic 2 type, where involutions resemble unipotent elements, and other groups, where involutions resemble semisimple elements. ...2 KB (298 words) - 23:33, 15 January 2024
- In mathematical finite group theory, the '''L-balance theorem''' was proved by {{harvtxt|Gorenstei The L-balance theorem of Gorenstein and Walter states that if ''X'' is a finite group and ''T'' a 2-subgroup of ''X'' then ...2 KB (240 words) - 09:56, 14 September 2024
- ...igman–Sims asymptotic formula''' gives an asymptotic estimate on number of groups of prime power order. ...mber]]. Define <math>f(n,p)</math> as the number of isomorphism classes of groups of order <math>p^n</math>. Then: ...1 KB (193 words) - 08:38, 27 December 2024
- {{Short description|Collection of groups}} ...oup|commutativity]]). Since [[set theory]] does not admit the "set of all groups", it is necessary to work with the more general concept of ''[[Class_(set_t ...5 KB (881 words) - 00:55, 2 March 2025
- ...[[abstract algebra]] known as [[group theory]], the '''diameter''' of a [[finite group]] is a measure of its complexity. Consider a finite group <math>\left(G,\circ\right)</math>, and any [[generating set of a grou ...2 KB (281 words) - 02:03, 31 August 2024
- {{about|graphs defined from finite groups|other uses|Glossary of graph theory#prime}} In the mathematics of [[graph theory]] and [[finite group]]s, a '''prime graph''' is an [[undirected graph]] defined from a [[G ...4 KB (572 words) - 03:45, 30 December 2024
- ...]] spanned by the [[double coset]]s ''HgH'' of a [[subgroup]] ''H'' of a [[finite group]] ''G''. It is a special case of a [[Hecke algebra of a locally compa ...tics)|field]] of [[characteristic (algebra)|characteristic]] zero, ''G'' a finite [[group (mathematics)|group]] and ''H'' a subgroup of ''G''. Let <math>F[G] ...2 KB (362 words) - 02:15, 15 May 2024
- {{unsolved|mathematics|Which finite groups are BI-groups?}} Let <math>G</math> be a finite group, let <math>\operatorname{Irr}(G)</math> be the set of all [[irreducib ...3 KB (361 words) - 08:39, 8 May 2024
- ...t2=Lucchini |first2=A. |date=1995-11-15 |title=Generation of Almost Simple Groups |url=https://www.sciencedirect.com/science/article/pii/S0021869385713452 |j * Trivially, non-abelian simple groups and the full group of automorphisms are almost simple. For <math>n=5</math> ...3 KB (485 words) - 18:28, 1 March 2025
- {{for|the finite simple group|Higman–Sims group}} ...(mathematics)|group]] with no [[trivial group|nontrivial]] [[finite group|finite]] [[quotient group|quotients]]. ...2 KB (246 words) - 02:11, 7 March 2024
- ...t1=Brauer |first1=Richard D. |year=1963 |chapter=Representations of finite groups |title=Lectures in Mathematics |volume=1 |publisher=Wiley | pages=133–175 | ...bgroups]], called the [[Modular representation theory#Defect groups|defect groups]] of <math>B</math>. The set of irreducible characters belonging to <math>B ...4 KB (520 words) - 09:23, 20 February 2025
- {{Short description|The probability that two uniform random elements of a finite group commute with each other}} ...finite group is. It can be generalized to infinite [[group (mathematics)|groups]] equipped with a suitable [[probability measure]],<ref name=":0" /> and ca ...4 KB (650 words) - 21:05, 25 February 2025
- ...he theory of [[Hall subgroup]]s and [[Carter subgroup]]s of [[finite group|finite]] [[solvable group]]s. ...roup|''p''-groups]] for a [[prime number|prime]] ''p'', the formation of π-groups for a set of primes π, and the formation of [[nilpotent group]]s. ...4 KB (484 words) - 14:18, 26 May 2024
- In [[mathematics]], a '''Leinster group''' is a [[finite group]] whose [[order (group theory)|order]] equals the sum of the orders o ...ster}} He called them "perfect groups"{{r|leinster}} and later "immaculate groups",{{r|brunault}} ...5 KB (716 words) - 17:26, 12 October 2024
- ...\times</math> are precisely the open subgroups of <math>K^\times</math> of finite index. ...595 bytes (96 words) - 09:14, 7 July 2024
- ...rtation ''Il Prime Graph dei gruppi finiti'' [''the prime graphs of finite groups''], supervised by Napolitani and co-advised by Carlo Casolo.{{r|sum|mg}} Lucido was particularly known for her research on [[prime graph]]s of [[finite group]]s. These are [[undirected graph]]s that have a vertex for each [[pri ...4 KB (580 words) - 03:46, 30 December 2024