Question

example of a non-abelian group $G$ and a non-trivial maximal normal subgroup $N$ so that $[G : N] ≥ 3$.

score 439 · Answer 1 · 2020-05-04 19:24:58

439

Views

example of a non-abelian group $G$ and a non-trivial maximal normal subgroup $N$ so that $[G : N] ≥ 3$.

Published on 04 May 2020 - 19:24

score 66 · Answer 2 · 2026-02-23 12:09:15

66

Views

On the number of invariant Sylow subgroups under coprime action -Antonio Beltrán, Changguo Shao

Published on 23 Feb 2026 - 12:09

score 184 · Answer 3 · 2016-07-22 05:43:47

184

Views

how to check if a subgroup is maximal?

Published on 22 Jul 2016 - 5:43

score 402 · Answer 4 · 2016-07-22 08:28:46

402

Views

cardinality of a maximal subgroup of a $p$ group

Published on 22 Jul 2016 - 8:28

score 961 · Answer 5 · 2016-08-18 19:46:05

961

Views

All maximal independent sets of a matroid have the same cardinality

Published on 18 Aug 2016 - 19:46

score 202 · Answer 6 · 2016-10-02 22:10:52

202

Views

Why is $A_n$ maximal in $S_n$?

Published on 02 Oct 2016 - 22:10

score 92 · Answer 7 · 2016-10-09 15:41:35

92

Views

If we have that H<G and |H|=|G| does this imply that H=G?

Published on 09 Oct 2016 - 15:41

score 1.3k · Answer 8 · 2016-11-04 15:07:18

1.3k

Views

Intersection of Maximal subgroups

Published on 04 Nov 2016 - 15:07

score 158 · Answer 9 · 2026-02-23 01:19:14

158

Views

Maximal (permutation) subgroups of $PSL(2,p)$

Published on 23 Feb 2026 - 1:19

score 55 · Answer 10 · 2016-12-18 15:46:42

55

Views

Stabilisers in non-abelian $p$-groups are contained in non-transitive maximal abelian subgroups?

Published on 18 Dec 2016 - 15:46

score 65 · Answer 11 · 2016-12-26 03:43:55

65

Views

Groups having no maximal cyclic subgroups of prime order

Published on 26 Dec 2016 - 3:43

score 224 · Answer 12 · 2017-01-01 14:37:07

224

Views

GAP/Magma-cas: Suppose $H<S_n$ (given by generators): Does either system make it easy to find the maximal subgroup containing $H$?

Published on 01 Jan 2017 - 14:37

score 868 · Answer 13 · 2017-02-26 02:38:54

868

Views

Maximal & Maximal Normal Subgroups

Published on 26 Feb 2017 - 2:38

score 325 · Answer 14 · 2017-03-17 20:53:30

325

Views

Are there necessary and sufficient conditions for any group to have a maximal normal subgroup?

Published on 17 Mar 2017 - 20:53

score 325 · Answer 15 · 2017-04-05 16:43:06

325

Views

$|G|=p^n$, $Z(G)=\langle w\rangle$, $Z(G)\subseteq$ a maximal subgroup; then $\exists f\in \operatorname{Aut}(G)\ , k\ne1\pmod p$ s.t. $ f(w)=w^k$?

Published on 05 Apr 2017 - 16:43

List Question

example of a non-abelian group $G$ and a non-trivial maximal normal subgroup $N$ so that $[G : N] ≥ 3$.

On the number of invariant Sylow subgroups under coprime action -Antonio Beltrán, Changguo Shao

how to check if a subgroup is maximal?

cardinality of a maximal subgroup of a $p$ group

All maximal independent sets of a matroid have the same cardinality

Why is $A_n$ maximal in $S_n$?

If we have that H<G and |H|=|G| does this imply that H=G?

Intersection of Maximal subgroups

Maximal (permutation) subgroups of $PSL(2,p)$

Stabilisers in non-abelian $p$-groups are contained in non-transitive maximal abelian subgroups?

Groups having no maximal cyclic subgroups of prime order

GAP/Magma-cas: Suppose $H<S_n$ (given by generators): Does either system make it easy to find the maximal subgroup containing $H$?

Maximal & Maximal Normal Subgroups

Are there necessary and sufficient conditions for any group to have a maximal normal subgroup?

$|G|=p^n$, $Z(G)=\langle w\rangle$, $Z(G)\subseteq$ a maximal subgroup; then $\exists f\in \operatorname{Aut}(G)\ , k\ne1\pmod p$ s.t. $ f(w)=w^k$?

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