Question

Normal simple subgroup

score 89 · Answer 1 · 2020-05-28 09:00:05

89

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Normal simple subgroup

Published on 28 May 2020 - 9:00

score 318 · Answer 2 · 2020-06-02 19:33:06

318

Views

Irreducible components are the building blocks?

Published on 02 Jun 2020 - 19:33

score 236 · Answer 3 · 2026-03-23 23:32:01

236

Views

Finite simple group has order a multiple of 3?

Published on 23 Mar 2026 - 23:32

score 502 · Answer 4 · 2020-07-11 16:49:51

502

Views

A Finite Group, $G$, Contains a Proper Subgroup of Index 2, Thus $G$ is not Simple

Published on 11 Jul 2020 - 16:49

score 381 · Answer 5 · 2026-03-25 06:03:53

381

Views

Let $G$ be a finite non-solvable group, each of whose proper subgroups is solvable.

Published on 25 Mar 2026 - 6:03

score 329 · Answer 6 · 2026-03-26 04:35:04

329

Views

A finite group $G$ is called an $N$-group if the normalizer $N_G(P)$ of every non-identity p-subgroup $P$ of $G$ is solvable.

Published on 26 Mar 2026 - 4:35

score 91 · Answer 7 · 2020-07-25 23:25:29

91

Views

a group $G$ whose order has exactly two prime divisors is not simple, Burnside theorem?

Published on 25 Jul 2020 - 23:25

score 548 · Answer 8 · 2016-07-12 21:26:59

548

Views

Infinite length Composition series

Published on 12 Jul 2016 - 21:26

score 423 · Answer 9 · 2016-08-10 22:08:26

423

Views

Developing Intuition for the Monster Group

Published on 10 Aug 2016 - 22:08

score 2.4k · Answer 10 · 2016-08-17 20:40:55

2.4k

Views

Is there a classification of infinite simple groups?

Published on 17 Aug 2016 - 20:40

score 29 · Answer 11 · 2016-08-21 19:16:09

29

Views

If $H_i \unlhd H_{i+1}$ and $N$ is simple then $H_iN \unlhd H_{i+1} N$

Published on 21 Aug 2016 - 19:16

score 612 · Answer 12 · 2016-09-02 16:24:16

612

Views

Simply connected semisimple algebraic group is a direct product of simply connected simple groups

Published on 02 Sep 2016 - 16:24

score 63 · Answer 13 · 2016-09-14 00:15:59

63

Views

Let G be simple, |G| is not 2, and ϕ a homomorphism from G to H. If H contains a normal subgroup A of index 2, then ϕ(G) ≤ A .

Published on 14 Sep 2016 - 0:15

score 220 · Answer 14 · 2016-09-26 00:32:14

220

Views

Suppose $N\unlhd G$ with $N\cong G/N\cong S$, $S$ a nonabelian finite simple group. Assume that $\operatorname{Out}(S)$ is solvable.

Published on 26 Sep 2016 - 0:32

score 281 · Answer 15 · 2016-09-28 21:04:38

281

Views

a lie algebra is semisimple if and only if it does not possess a non-zero solvable ideal?

Published on 28 Sep 2016 - 21:04

List Question

Normal simple subgroup

Irreducible components are the building blocks?

Finite simple group has order a multiple of 3?

A Finite Group, $G$, Contains a Proper Subgroup of Index 2, Thus $G$ is not Simple

Let $G$ be a finite non-solvable group, each of whose proper subgroups is solvable.

A finite group $G$ is called an $N$-group if the normalizer $N_G(P)$ of every non-identity p-subgroup $P$ of $G$ is solvable.

a group $G$ whose order has exactly two prime divisors is not simple, Burnside theorem?

Infinite length Composition series

Developing Intuition for the Monster Group

Is there a classification of infinite simple groups?

If $H_i \unlhd H_{i+1}$ and $N$ is simple then $H_iN \unlhd H_{i+1} N$

Simply connected semisimple algebraic group is a direct product of simply connected simple groups

Let G be simple, |G| is not 2, and ϕ a homomorphism from G to H. If H contains a normal subgroup A of index 2, then ϕ(G) ≤ A .

Suppose $N\unlhd G$ with $N\cong G/N\cong S$, $S$ a nonabelian finite simple group. Assume that $\operatorname{Out}(S)$ is solvable.

a lie algebra is semisimple if and only if it does not possess a non-zero solvable ideal?

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