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  • * 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 also
    7 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-case
    3 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 accessibl
    2 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. Brown
    721 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 attra
    3 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 242-2
    987 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</math
    4 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 so
    519 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. For
    2 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 o
    8 KB (1,234 words) - 05:31, 21 January 2013

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