Question

Let $G$ be a finite simple group. Suppose that $H$ is a subgroup of $G$ with index $n=|G:H|>1$. Show that $|H|$ divides $(n-1)!$

score 1.8k · Answer 1 · 2014-05-15 06:20:40

1.8k

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Let $G$ be a finite simple group. Suppose that $H$ is a subgroup of $G$ with index $n=|G:H|>1$. Show that $|H|$ divides $(n-1)!$

Published on 15 May 2014 - 6:20

score 165 · Answer 2 · 2014-06-11 13:05:25

165

Views

Simple non-abelian groups

Published on 11 Jun 2014 - 13:05

score 550 · Answer 3 · 2014-06-12 06:32:22

550

Views

regular unipotent elements

Published on 12 Jun 2014 - 6:32

score 1.1k · Answer 4 · 2026-03-19 10:55:32

1.1k

Views

Sylow $p$-subgroups of finite simple groups of Lie type

Published on 19 Mar 2026 - 10:55

score 237 · Answer 5 · 2014-06-14 17:13:46

237

Views

The center of Sylow $p$-subgroups of a finite simple group of Lie type

Published on 14 Jun 2014 - 17:13

score 68 · Answer 6 · 2014-06-17 15:14:34

68

Views

Using a theorem to find the center of a $p$-sylow subgroup of simple group

Published on 17 Jun 2014 - 15:14

score 191 · Answer 7 · 2014-06-20 15:29:21

191

Views

Simple groups of order 7920

Published on 20 Jun 2014 - 15:29

score 6.6k · Answer 8 · 2014-06-22 06:42:53

6.6k

Views

Examples of Infinite Simple Groups

Published on 22 Jun 2014 - 6:42

score 50 · Answer 9 · 2014-06-26 15:02:32

50

Views

Some things about maximal tori

Published on 26 Jun 2014 - 15:02

score 354 · Answer 10 · 2014-07-10 09:47:45

354

Views

Simple groups with cyclic odd Sylow subgroups

Published on 10 Jul 2014 - 9:47

score 186 · Answer 11 · 2014-07-29 10:34:47

186

Views

Projective special linear groups are co-hopfian?

Published on 29 Jul 2014 - 10:34

score 1.5k · Answer 12 · 2014-07-30 18:44:32

1.5k

Views

How to prove that every nonabelian group of odd order is not simple?

Published on 30 Jul 2014 - 18:44

score 137 · Answer 13 · 2014-08-12 18:36:25

Elements of $\operatorname{Aut}(\operatorname{Aut}(G))$ acting as an identity on $\operatorname{Inn}(G)$, for $G$ a nonabelian, simple group

score 1.4k · Answer 14 · 2014-08-18 18:47:20

1.4k

Views

How do we know the classification of finite simple groups is finished?

Published on 18 Aug 2014 - 18:47

score 73 · Answer 15 · 2014-09-13 18:36:52

73

Views

Sufficiently transitive implies alternating sans Enormous Theorem

Published on 13 Sep 2014 - 18:36

List Question

Let $G$ be a finite simple group. Suppose that $H$ is a subgroup of $G$ with index $n=|G:H|>1$. Show that $|H|$ divides $(n-1)!$

Simple non-abelian groups

regular unipotent elements

Sylow $p$-subgroups of finite simple groups of Lie type

The center of Sylow $p$-subgroups of a finite simple group of Lie type

Using a theorem to find the center of a $p$-sylow subgroup of simple group

Simple groups of order 7920

Examples of Infinite Simple Groups

Some things about maximal tori

Simple groups with cyclic odd Sylow subgroups

Projective special linear groups are co-hopfian?

How to prove that every nonabelian group of odd order is not simple?

Elements of $\operatorname{Aut}(\operatorname{Aut}(G))$ acting as an identity on $\operatorname{Inn}(G)$, for $G$ a nonabelian, simple group

How do we know the classification of finite simple groups is finished?

Sufficiently transitive implies alternating sans Enormous Theorem

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