# Search results

## Page title matches

• ...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
• This category lists pages on the element structures of group families. [[Category:Specific information about group families]]
57 members (0 subcategories, 0 files) - 16:49, 2 November 2010
• Extremely important and basic group families (importance rank 1): {{#ask:[[Category:Linear representation theory of group families]][[Specific information about.Importance rank::1]]|?Specific information ab
53 members (0 subcategories, 0 files) - 03:19, 5 December 2011
• 6 members (6 subcategories, 0 files) - 01:08, 11 November 2010
• ...mation about supergroups of groups in various kinds of families, where the families may be specified by order, by a particular kind of presentation, or by havi [[Category:Specific information about group families]]
0 members (0 subcategories, 0 files) - 00:15, 12 April 2011
• This category lists pages on the subgroup structures of group families. [[Category:Specific information about group families]]
16 members (0 subcategories, 0 files) - 14:20, 19 June 2011
• [[Category:Specific information about group families]]
2 members (0 subcategories, 0 files) - 07:56, 20 May 2012
• [[Category:Specific information about group families]]
24 members (0 subcategories, 0 files) - 19:45, 20 January 2013

## Page text matches

• ...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 [itex]e[/itex] and [itex]x[/itex] such that [itex]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 [itex]G[/itex] be a finite group and [itex]p[/itex] a [[prime number]] dividing the order of [itex]G[/itex]. The McKay conjecture holds trivially for [[finite nilpotent group]]s, because each Sylow subgroup is normal and hence [itex]G = N_G(P)[/itex]
2 KB (377 words) - 00:32, 10 May 2011
• {{prime-parametrized particular group}} Note that the case [itex]p = 2[/itex], 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 [itex]p = 3[/itex] (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 [itex]GL(2,5)[/itex] 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 [itex]G[/itex], denoted [itex]M(G)[/itex], is an [[abelian group]] defined in the following equivalent ways: ...roup || It is the second [[defining ingredient::homology group for trivial group action]] [itex]\! H_2(G;\mathbb{Z})[/itex].
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 [itex]G[/itex] is simple if ...
10 KB (1,387 words) - 20:01, 23 April 2014
• The symmetric group [itex]S_3[/itex] 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 [itex]\operatorname{Sym}(4)[/itex], 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]] [itex]PSL(4,2)[/itex]) 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 [itex]G[/itex] is a [[finite group]], [itex]p[/itex] is a prime, and [itex]P[/itex] is a [itex]p[/itex]-[[Sylo [itex]G[/itex] is a [[finite group]], [itex]p[/itex] is a prime, and [itex]P[/itex] is a [itex]p[/itex]-[[Sylo
1 KB (222 words) - 20:50, 10 March 2009

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