Question

Need help in understanding a certain step of a certain proof in finite group theory and group actions

score 230 · Answer 1 · 2016-06-24 20:08:27

230

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Need help in understanding a certain step of a certain proof in finite group theory and group actions

Published on 24 Jun 2016 - 20:08

score 278 · Answer 2 · 2016-06-25 07:32:53

278

Views

A simple group such that $[G:H]=n$ can be embedded into $A_n$

Published on 25 Jun 2016 - 7:32

score 198 · Answer 3 · 2016-06-25 22:11:26

198

Views

$G \cong H$ and $G$ is simple. Then $H$ is simple as well.

Published on 25 Jun 2016 - 22:11

score 2k · Answer 4 · 2016-06-30 00:36:34

2k

Views

A group is simple if an only if its homomorphic images are the trivial group and $G$ itself (up to isomorphism)

Published on 30 Jun 2016 - 0:36

score 332 · Answer 5 · 2026-03-26 04:49:29

332

Views

Examples of profinite simple groups

Published on 26 Mar 2026 - 4:49

score 964 · Answer 6 · 2013-04-01 23:35:23

964

Views

How confident can we be about the validity of the classification of finite simple groups?

Published on 01 Apr 2013 - 23:35

score 4.5k · Answer 7 · 2013-04-08 14:27:47

4.5k

Views

Definition of Simple Group

Published on 08 Apr 2013 - 14:27

score 2.2k · Answer 8 · 2013-04-10 10:38:07

2.2k

Views

Group of order 9 is simple

Published on 10 Apr 2013 - 10:38

score 3k · Answer 9 · 2013-04-10 15:37:05

3k

Views

Subgroups of $A_5$ have order at most $12$?

Published on 10 Apr 2013 - 15:37

score 301 · Answer 10 · 2026-03-27 07:11:39

301

Views

Projective linear group - solvable

Published on 27 Mar 2026 - 7:11

score 1.9k · Answer 11 · 2013-04-15 15:19:33

1.9k

Views

Why is the Monster group the largest sporadic finite simple group?

Published on 15 Apr 2013 - 15:19

score 557 · Answer 12 · 2013-04-22 06:59:40

557

Views

Simple groups some interesting properties

Published on 22 Apr 2013 - 6:59

score 1.7k · Answer 13 · 2013-04-30 15:01:29

1.7k

Views

Groups of order 8 are not simple

Published on 30 Apr 2013 - 15:01

score 1.5k · Answer 14 · 2013-05-21 15:57:24

1.5k

Views

Let $G$ be a simple group of order $n$. Let $H$ be a subgroup of $G$ of index $k$. Show that $n$ divides $k!$

Published on 21 May 2013 - 15:57

score 218 · Answer 15 · 2013-05-22 16:30:03

218

Views

Are the quotient groups in a composition sequence necessarily subgroups?

Published on 22 May 2013 - 16:30

List Question

Need help in understanding a certain step of a certain proof in finite group theory and group actions

A simple group such that $[G:H]=n$ can be embedded into $A_n$

$G \cong H$ and $G$ is simple. Then $H$ is simple as well.

A group is simple if an only if its homomorphic images are the trivial group and $G$ itself (up to isomorphism)

Examples of profinite simple groups

How confident can we be about the validity of the classification of finite simple groups?

Definition of Simple Group

Group of order 9 is simple

Subgroups of $A_5$ have order at most $12$?

Projective linear group - solvable

Why is the Monster group the largest sporadic finite simple group?

Simple groups some interesting properties

Groups of order 8 are not simple

Let $G$ be a simple group of order $n$. Let $H$ be a subgroup of $G$ of index $k$. Show that $n$ divides $k!$

Are the quotient groups in a composition sequence necessarily subgroups?

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