Question

What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity?

score 265 · Answer 1 · 2026-03-25 07:48:42

265

Views

What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity?

Published on 25 Mar 2026 - 7:48

score 101 · Answer 2 · 2026-03-25 07:45:45

101

Views

The Frattini subgroup of the standard Wreath product of two quasicyclic groups is the group itself.

Published on 25 Mar 2026 - 7:45

score 230 · Answer 3 · 2022-01-05 14:08:54

230

Views

Understanding the definition of Sylow $p$-subgroups

Published on 05 Jan 2022 - 14:08

score 180 · Answer 4 · 2022-01-08 07:01:29

180

Views

Zorn's lemma and maximal elements

Published on 08 Jan 2022 - 7:01

score 199 · Answer 5 · 2022-01-25 05:56:46

199

Views

Maximal cyclic subgroups

Published on 25 Jan 2022 - 5:56

score 286 · Answer 6 · 2022-03-01 12:32:07

286

Views

Show $S_n$ is a primitive permutation group.

Published on 01 Mar 2022 - 12:32

score 46 · Answer 7 · 2022-04-12 06:23:58

46

Views

If $H$ is a maximal subgroup of $G$, then the action of $G$ on the cosets of $H$ is primitive.

Published on 12 Apr 2022 - 6:23

score 178 · Answer 8 · 2022-04-21 20:40:28

178

Views

Let $G$ be a finite group and $M$ be a maximal subgroup of $G$. If $G = Z(G)M$, then $M$ is normal in $G$

Published on 21 Apr 2022 - 20:40

score 33 · Answer 9 · 2022-04-22 17:50:08

33

Views

Let $S$ be any non-empty subset of a group $G$. Does there exists a UNIQUE MAXIMAL subgroup $H$ such that $S$ is union of (some) left cosets of $H$?

Published on 22 Apr 2022 - 17:50

score 233 · Answer 10 · 2026-03-25 06:10:26

233

Views

Maximal compact subgroups of $\mathrm{GL}(2,\mathbb Q_p)$

Published on 25 Mar 2026 - 6:10

score 222 · Answer 11 · 2022-07-11 17:09:45

222

Views

Let $H$ be a maximal subgroup of a finite group $G$ such that $|G:H|=4$. Then there exists $K\leq H$ such that $|H:K|=3$

Published on 11 Jul 2022 - 17:09

score 332 · Answer 12 · 2026-03-25 14:43:16

332

Views

Every maximal subgroup has prime index.

Published on 25 Mar 2026 - 14:43

score 91 · Answer 13 · 2022-08-03 12:07:53

91

Views

A question on a 2-group with an elementary Abelian maximal subgroup

Published on 03 Aug 2022 - 12:07

score 54 · Answer 14 · 2026-02-23 04:55:02

54

Views

inclusion among finite symplectic groups

Published on 23 Feb 2026 - 4:55

score 76 · Answer 15 · 2026-02-23 06:36:24

76

Views

construct the normaliser of a subgroup and then construct the subgroup

Published on 23 Feb 2026 - 6:36

List Question

What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity?

The Frattini subgroup of the standard Wreath product of two quasicyclic groups is the group itself.

Understanding the definition of Sylow $p$-subgroups

Zorn's lemma and maximal elements

Maximal cyclic subgroups

Show $S_n$ is a primitive permutation group.

If $H$ is a maximal subgroup of $G$, then the action of $G$ on the cosets of $H$ is primitive.

Let $G$ be a finite group and $M$ be a maximal subgroup of $G$. If $G = Z(G)M$, then $M$ is normal in $G$

Let $S$ be any non-empty subset of a group $G$. Does there exists a UNIQUE MAXIMAL subgroup $H$ such that $S$ is union of (some) left cosets of $H$?

Maximal compact subgroups of $\mathrm{GL}(2,\mathbb Q_p)$

Let $H$ be a maximal subgroup of a finite group $G$ such that $|G:H|=4$. Then there exists $K\leq H$ such that $|H:K|=3$

Every maximal subgroup has prime index.

A question on a 2-group with an elementary Abelian maximal subgroup

inclusion among finite symplectic groups

construct the normaliser of a subgroup and then construct the subgroup

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