Question

$G$ be a finite simple group and $H,K$ be subgroups of prime index ; then is it true that $H,K$ are of same size?

score 710 · Answer 1 · 2015-10-09 12:20:02

710

Views

$G$ be a finite simple group and $H,K$ be subgroups of prime index ; then is it true that $H,K$ are of same size?

Published on 09 Oct 2015 - 12:20

score 1k · Answer 2 · 2015-10-12 22:02:45

1k

Views

A question about the composition series of two particular isomorphic groups

Published on 12 Oct 2015 - 22:02

score 217 · Answer 3 · 2015-10-20 21:40:00

217

Views

Why does $A_\infty=\bigcup_{n\geq 5}^{\infty} \,A_n$?

Published on 20 Oct 2015 - 21:40

score 1.1k · Answer 4 · 2026-03-25 08:22:04

1.1k

Views

$A_4$ is not simple

Published on 25 Mar 2026 - 8:22

score 48 · Answer 5 · 2015-10-28 01:25:02

48

Views

$G\times H$ is not a simple group for $|G|, |H|\geq 2$

Published on 28 Oct 2015 - 1:25

score 48 · Answer 6 · 2015-10-31 23:19:54

48

Views

No simple subgroups in common implies order of groups relatively prime?

Published on 31 Oct 2015 - 23:19

score 151 · Answer 7 · 2015-11-01 21:07:55

151

Views

Subgroup $Q$ of $M\times M'$ is not a direct product of subgroups of $M$ & $M'$, do $M$ and $M'$ share no simple subgroups?

Published on 01 Nov 2015 - 21:07

score 105 · Answer 8 · 2026-03-23 23:31:33

105

Views

A group G with order $15$ is simple?

Published on 23 Mar 2026 - 23:31

score 812 · Answer 9 · 2026-03-11 22:56:03

812

Views

$PSL(n,q)$ is simple: Proof

Published on 11 Mar 2026 - 22:56

score 167 · Answer 10 · 2015-11-19 02:07:07

167

Views

Proof of existence of simple group of Order 168 in Dummit and Foote

Published on 19 Nov 2015 - 2:07

score 180 · Answer 11 · 2015-11-30 20:57:02

180

Views

Normal simple subgroups and composition series

Published on 30 Nov 2015 - 20:57

score 456 · Answer 12 · 2026-03-24 15:22:59

456

Views

Show that there does not exist a simple group of order $126$.

Published on 24 Mar 2026 - 15:22

score 121 · Answer 13 · 2015-12-18 15:32:10

121

Views

Simplicity of homeomorphism group

Published on 18 Dec 2015 - 15:32

score 121 · Answer 14 · 2015-12-19 07:32:18

121

Views

Limitations on the structures of normal subgroups and generating a n-degree polynomial formula

Published on 19 Dec 2015 - 7:32

score 662 · Answer 15 · 2015-12-24 02:46:20

662

Views

Historical notes on the Jordan-Hölder program

Published on 24 Dec 2015 - 2:46

List Question

$G$ be a finite simple group and $H,K$ be subgroups of prime index ; then is it true that $H,K$ are of same size?

A question about the composition series of two particular isomorphic groups

Why does $A_\infty=\bigcup_{n\geq 5}^{\infty} \,A_n$?

$A_4$ is not simple

$G\times H$ is not a simple group for $|G|, |H|\geq 2$

No simple subgroups in common implies order of groups relatively prime?

Subgroup $Q$ of $M\times M'$ is not a direct product of subgroups of $M$ & $M'$, do $M$ and $M'$ share no simple subgroups?

A group G with order $15$ is simple?

$PSL(n,q)$ is simple: Proof

Proof of existence of simple group of Order 168 in Dummit and Foote

Normal simple subgroups and composition series

Show that there does not exist a simple group of order $126$.

Simplicity of homeomorphism group

Limitations on the structures of normal subgroups and generating a n-degree polynomial formula

Historical notes on the Jordan-Hölder program

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