Question

Are all simple groups solvable?

score 1.3k · Answer 1 · 2026-03-27 23:38:23

1.3k

Views

Are all simple groups solvable?

Published on 27 Mar 2026 - 23:38

score 205 · Answer 2 · 2021-04-12 14:14:55

205

Views

Help understanding composition series with non-abelian group having factor groups being abelian

Published on 12 Apr 2021 - 14:14

score 110 · Answer 3 · 2021-04-20 22:50:08

110

Views

Is the group of outer class-preserving automorphisms of a finite group soluble?

Published on 20 Apr 2021 - 22:50

score 583 · Answer 4 · 2021-04-26 10:58:54

583

Views

Let $G$ and $H$ be nontrivial groups such that $G$ is simple and let $f : G \to H$ be a surjective homomorphism. Show that $f$ is an isomorphism.

Published on 26 Apr 2021 - 10:58

score 63 · Answer 5 · 2021-05-10 14:20:16

63

Views

Why is this a homomorphism (proof of no simple groups order 144)

Published on 10 May 2021 - 14:20

score 91 · Answer 6 · 2021-05-14 18:28:51

91

Views

There is no simple group of order 400

Published on 14 May 2021 - 18:28

score 420 · Answer 7 · 2026-03-28 06:40:43

420

Views

Show that a group of order $175$ is not simple.

Published on 28 Mar 2026 - 6:40

score 39 · Answer 8 · 2021-05-29 07:34:19

39

Views

number theory argument needed for equation for the size of a simple group

Published on 29 May 2021 - 7:34

score 124 · Answer 9 · 2021-06-11 18:15:02

124

Views

some particular extensions of $SL_2(5)$

Published on 11 Jun 2021 - 18:15

score 182 · Answer 10 · 2021-06-13 12:00:47

182

Views

Why does the MOG provide the octads of a Steiner system

Published on 13 Jun 2021 - 12:00

score 95 · Answer 11 · 2021-06-21 05:42:39

95

Views

Simple subgroup of $S_{n+1}$ of index k

Published on 21 Jun 2021 - 5:42

score 117 · Answer 12 · 2026-02-23 09:32:13

117

Views

Let $G$ be a finite group. Then $G$ is completely reducible iff $G={\rm Soc}(G)$.

Published on 23 Feb 2026 - 9:32

score 341 · Answer 13 · 2021-06-25 12:22:11

341

Views

Let $G$ be the direct product of two nonabelian simple groups. Then $G$ has exactly four normal subgroups

Published on 25 Jun 2021 - 12:22

score 333 · Answer 14 · 2021-06-28 03:11:29

333

Views

Let $G$ be a group and $H\unlhd G$. Prove that if $G/H$ is a simple group, then $G\neq H$ and $\not\exists K$ s.t. $H\leq K\leq G,K \unlhd G.$

Published on 28 Jun 2021 - 3:11

score 59 · Answer 15 · 2021-06-28 22:27:36

59

Views

The image of a completely reducible group is itself completely reducible.

Published on 28 Jun 2021 - 22:27

List Question

Are all simple groups solvable?

Help understanding composition series with non-abelian group having factor groups being abelian

Is the group of outer class-preserving automorphisms of a finite group soluble?

Let $G$ and $H$ be nontrivial groups such that $G$ is simple and let $f : G \to H$ be a surjective homomorphism. Show that $f$ is an isomorphism.

Why is this a homomorphism (proof of no simple groups order 144)

There is no simple group of order 400

Show that a group of order $175$ is not simple.

number theory argument needed for equation for the size of a simple group

some particular extensions of $SL_2(5)$

Why does the MOG provide the octads of a Steiner system

Simple subgroup of $S_{n+1}$ of index k

Let $G$ be a finite group. Then $G$ is completely reducible iff $G={\rm Soc}(G)$.

Let $G$ be the direct product of two nonabelian simple groups. Then $G$ has exactly four normal subgroups

Let $G$ be a group and $H\unlhd G$. Prove that if $G/H$ is a simple group, then $G\neq H$ and $\not\exists K$ s.t. $H\leq K\leq G,K \unlhd G.$

The image of a completely reducible group is itself completely reducible.

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