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## Page title matches

- ...ups of prime power order'' refers to the problem of enumerating all finite groups of order <math>p^n</math> where <math>p</math> is a prime and <math>n</math which returns the number of groups of order <math>p^n</math>. The following facts are known about <math>f(n,p)1 KB (222 words) - 03:25, 26 December 2011
- #REDIRECT [[Neumann's open problem on number of projective special linear groups whose order has exactly six prime factors counting multiplicities]]148 bytes (20 words) - 12:46, 19 June 2011
- ...(Note that if <math>P</math> is the wreath product of <math>n</math> such groups, <math>P</math> is isomorphic to the <math>p</math>-Sylow subgroup of the s934 bytes (162 words) - 13:15, 12 October 2008
- * [[Classification of finite simple groups whose order has at most five prime factors counting muliplicities]]638 bytes (97 words) - 12:47, 19 June 2011
- Let <math>\mathcal{S}</math> be the collection of groups of order <math>p^p</math> and exponent <math>p</math>. Then, <math>\mathcal{S}</math> is ''not'' a [[fact about::collection of groups satisfying a weak normal replacement condition]] for the prime <math>p</mat317 bytes (54 words) - 03:47, 14 May 2009
- #REDIRECT [[Collection of groups of prime-to-the-prime order and prime exponent does not satisfy weak normal132 bytes (17 words) - 03:47, 14 May 2009
- 9 members (0 subcategories, 0 files) - 00:09, 12 April 2011
- {{further|[[Particular example::wreath product of groups of order p]]}}1 KB (164 words) - 21:34, 31 July 2009
- {{prime-parametrized particular group}} ...ds, it is the free product in the sense of [[group of nilpotency class two|groups of nilpotency class two]] of two copies of the elementary abelian subgroup2 KB (331 words) - 21:52, 1 October 2009
- {{prime-parametrized particular group}} Particular cases are [[nontrivial semidirect product of Z4 and Z4]] for <math>p = 2</m893 bytes (142 words) - 15:13, 4 April 2010
- * [[Orbital maximin equals size of set for abelian groups]] ...tant fraction of number of ordered pairs of distinct elements for solvable groups]]1 KB (195 words) - 00:50, 11 February 2010
- ...l maximin equals number of ordered pairs of distinct elements for solvable groups iff size is prime power]]125 bytes (19 words) - 00:26, 11 February 2010
- ...ider the [[fact about::orbital maximax problem]] for finite <math>p</math>-groups acting on a set <math>S</math> of size <math>n</math>: we want to find the | [[abelian group]] || [[Orbital maximax equals size of set for abelian groups]]2 KB (244 words) - 01:25, 11 February 2010
- ...der <math>p^n</math> (see also [[group of prime power order]], [[number of groups of given order]]). Then: ...der <math>p^n</math> (see also [[group of prime power order]], [[number of groups of given order]]). Define:858 bytes (155 words) - 18:54, 31 December 2011
- ...fferent -- see [[groups of order 8]] for a summary of information on these groups. ...|Want to know how this list of groups is obtained? See [[classification of groups of prime-cube order]]}}16 KB (2,050 words) - 22:25, 16 August 2012
- ...tency class and order determine degrees of irreducible representations for groups up to prime-fourth order]] ...ncy class and order need not determine conjugacy class size statistics for groups of prime-fifth order]]1 KB (205 words) - 14:22, 17 June 2011
- * [[Nilpotency class and order determine conjugacy class size statistics for groups up to prime-fourth order]]1 KB (144 words) - 14:22, 17 June 2011
- ...] over a field of size 5, 7, 11, or 13, i.e,. <math>G</math> is one of the groups <math>PSL(2,5)</math>, <math>PSL(2,7)</math>, <math>PSL(2,11)</math>, and < * [[Neumann's open problem on number of projective special linear groups whose order has exactly six prime factors counting multiplicities]]2 KB (247 words) - 12:57, 19 June 2011
- Let <math>p</math> be a [[prime number]]. There are two groups of order <math>p^2</math>, namely: ...t these are the only groups of prime-square order, see [[classification of groups of prime-square order]].1 KB (178 words) - 17:54, 18 July 2010
- ...[prime number]]. Then there are, up to [[isomorphism of groups]], only two groups of order <math>p^2</math>: Note that both of these are abelian groups, so in particular we see that any prime-square is an [[fact about::abelianness-forcing number5 KB (787 words) - 23:13, 4 September 2012

## Page text matches

- * Being [[solvable group|solvable]] is a ''property'' over the collection of groups. In other words, every [[group]] either ''has'' the property of being solva ...roups is [[subgroup-closed group property|subgroup-closed]]. A property of groups is termed subgroup-closed if any subgroup of a group with the property also7 KB (1,067 words) - 22:24, 7 May 2008
- ...tance, a particular breed of dog, or a particular property of groups, or a particular type of number) then it should give a clear differentiating criterion. ...o subgroups ar enot introduced. Rather, constructs of natural language, in particular, the pronoun ''it'', are used.8 KB (1,260 words) - 11:15, 20 June 2008
- ...rems proved so far in mathematics is the [[classification of finite simple groups]], whose proof runs to 15,000 pages over several journals. Even the newer, ...nformation, whatever, information you want, on each of the sporadic simple groups. Further, the Classification splits results into various cases and sub-case3 KB (466 words) - 22:43, 7 May 2008
- * Being [[solvable group|solvable]] is a ''property'' over the collection of groups. In other words, every [[group]] either ''has'' the property of being solva ...common features that we may observe between different objects of study. In particular:4 KB (575 words) - 22:44, 7 May 2008
- ...ways groups and subgroups could be related, and in search of ''trivia'' on groups. I now wanted it to be in a form that was immediately and readily accessibl2 KB (398 words) - 22:44, 7 May 2008
- ...Particular cases are the [[multiplicative group of a finite field]] and in particular the [[multiplicative group of a prime field]].899 bytes (136 words) - 21:08, 25 June 2013
- {{complex wrt groups}} * ''Euler characteristics of groups'' by Kenneth S. Brown721 bytes (123 words) - 23:12, 7 May 2008
- ===Related fact on p-groups===2 KB (347 words) - 03:10, 6 July 2019
- The '''Third International Conference on the Theory of Groups and Related Topics''' was held at the Australian National University in Can ...included miniconferences on [[group representation]]s, on computations in groups, on [[solvable group]]s and on Burnside questions. The Program, which attra3 KB (395 words) - 23:13, 7 May 2008
- ...nter of a group. They may be satisfied by the center for a large number of groups. ==In groups with additional structure==15 KB (2,081 words) - 20:14, 1 June 2016
- The term was first used in the paper ''Transfer and fusion in finite groups'' by Finkel and Gorenstein in the Journal of Algebra, 6 (1967), Pages 242-2987 bytes (169 words) - 23:14, 7 May 2008
- {{functor from groups}}594 bytes (105 words) - 23:14, 7 May 2008
- ...[[direct factor is transitive]] || Suppose <math>H \le K \le G</math> are groups such that <math>H</math> is a characteristic direct factor of <math>K</math4 KB (455 words) - 02:59, 20 January 2013
- The term was first used in the paper ''Transfer and fusion in finite groups'' by Alperin and Gorenstein in the Journal of Algebra, 6 (1967), Pages 242- ...nstein|288|Chapter 8 (''p-constrained and p-stable groups''), Section 4 (''groups with subgroups of Glauberman type'')}}1 KB (186 words) - 17:39, 6 July 2013
- If two [[finite group]]s have relatively prime [[order]]s, then one of the groups is [[solvable group|solvable]]. For a complete list of applications, see [[:Category:Facts about groups of coprime order whose proof requires the assumption that one of them is so519 bytes (69 words) - 13:53, 20 August 2011
- ...wconstraints.pdf Using Sylow theory in the classification of finite simple groups]2 KB (413 words) - 23:24, 7 May 2008
- {{prime-parametrized sdf}} ...G</math> but only the order of <math>G</math>, it may happen that for some groups with that order, the core is trivial while for others it is nontrivial. For2 KB (287 words) - 23:24, 7 May 2008
- ...an endomorphism. Here are some related facts about <math>n</math>-abelian groups. {{#lst:n-abelian group|particular values}}3 KB (512 words) - 20:12, 10 August 2012
- | 1 || modular arithmetic definition || it is either [[isomorphic groups|isomorphic]] to the [[group of integers]] or to the [[group of integers mod | 3 || quotient of group of integers || it is [[isomorphic groups|isomorphic]] to a [[quotient map|quotient]] of the [[group of integers]] ||8 KB (1,111 words) - 23:25, 20 June 2013
- {{particular group}} * The {{symmetric group}} on two elements. In particular, it is a [[member of family::symmetric group on finite set]] and [[member o8 KB (1,234 words) - 05:31, 21 January 2013