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  • ...ral numbers. This means that for each natural number, there is exactly one group upto isomorphism in that family. Please also check [[:Category:Natural number-parametrized group properties]]
    3 members (0 subcategories, 0 files) - 23:46, 11 April 2011
  • ...operties parametrized by the natural numbers. Also check [[:Category:Group families parametrized by natural numbers]].
    14 members (0 subcategories, 0 files) - 23:37, 11 April 2011
  • Important group properties, sorted by importance rank: * [[:Category:Properties of subgroup families]]
    735 members (7 subcategories, 0 files) - 03:13, 17 December 2011
  • {{particular group}} ...ined as the unique group of order two. Explicitly it can be described as a group with two elements, say <math>e</math> and <math>x</math> such that <math>ex
    8 KB (1,234 words) - 05:31, 21 January 2013
  • ...]], so only one representation is considered per equivalence class) of the group, the [[defining ingredient::degree of a representation|degree]] of that rep ===Typical context: finite group and splitting field===
    15 KB (2,038 words) - 02:28, 28 May 2013
  • {{group eqrel}} ...een them, i.e., there is an isomorphism between their [[inner automorphism group]]s as well as an isomorphism between their [[derived subgroup]]s such that
    9 KB (1,243 words) - 16:41, 29 June 2013
  • Let <math>G</math> be a finite group and <math>p</math> a [[prime number]] dividing the order of <math>G</math>. The McKay conjecture holds trivially for [[finite nilpotent group]]s, because each Sylow subgroup is normal and hence <math>G = N_G(P)</math>
    2 KB (377 words) - 00:32, 10 May 2011
  • {{prime-parametrized particular group}} Note that the case <math>p = 2</math>, where the group becomes [[dihedral group:D8]], behaves somewhat differently from the general case. We note on the pa
    10 KB (1,463 words) - 11:21, 22 August 2014
  • {{prime-parametrized particular group}} ...matrix group:UT(4,2)]]) and <math>p = 3</math> (see [[unitriangular matrix group:UT(4,3)]]) differ somewhat from the cases of other primes. This is noted at
    5 KB (654 words) - 15:36, 18 September 2012
  • | [[General linear group over a field]] || Order of <math>GL(2,5)</math> incorrectly stated as 240 i | [[Projective special linear group]] || Wrote wrong prime factorization of 360 || || [https://groupprops.subwi
    55 KB (7,893 words) - 14:36, 6 July 2019
  • ...r''' of a group <math>G</math>, denoted <math>M(G)</math>, is an [[abelian group]] defined in the following equivalent ways: ...roup || It is the second [[defining ingredient::homology group for trivial group action]] <math>\! H_2(G;\mathbb{Z})</math>.
    8 KB (1,172 words) - 18:29, 29 June 2013
  • ...number among groups, group without any proper nontrivial normal subgroup, group without any proper nontrivial quotients}} ! No. !! Shorthand !! A group is simple if ... !! A group <math>G</math> is simple if ...
    10 KB (1,387 words) - 20:01, 23 April 2014
  • The symmetric group <math>S_3</math> can be defined in the following equivalent ways: ...amily::symmetric group of prime degree]] and [[member of family::symmetric group of prime power degree]].
    18 KB (2,584 words) - 16:41, 18 January 2015
  • {{particular group}} .../math> or <math>\operatorname{Sym}(4)</math>, also termed the '''symmetric group of degree four''', is defined in the following equivalent ways:
    16 KB (2,214 words) - 17:29, 19 May 2014
  • ...rist ('''G''') and a mathematics student ('''M''') who wants to know about group theory. '''G''': As of now, I'm interested in [[group theory]], particularly finite groups.
    4 KB (625 words) - 00:34, 8 May 2008
  • first = dihedral group:D8| second = quaternion group}}
    5 KB (737 words) - 14:04, 7 September 2011
  • ...cial linear group]] <math>PSL(4,2)</math>) and [[projective special linear group:PSL(3,4)]]. ===Infinite families===
    2 KB (321 words) - 02:30, 9 November 2011
  • {{group property}} A [[group]] is said to be '''ambivalent''' if every element in it is [[defining ingre
    7 KB (909 words) - 03:35, 13 January 2013
  • ...teen infinite families of simple groups, or to one of 26 [[sporadic simple group]]s. ==The eighteen families==
    12 KB (1,616 words) - 23:44, 12 September 2012
  • Suppose <math>G</math> is a [[finite group]], <math>p</math> is a prime, and <math>P</math> is a <math>p</math>-[[Sylo <math>G</math> is a [[finite group]], <math>p</math> is a prime, and <math>P</math> is a <math>p</math>-[[Sylo
    1 KB (222 words) - 20:50, 10 March 2009

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