Question

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

score 440 · Answer 1 · 2026-03-25 04:41:41

440

Views

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

Published on 25 Mar 2026 - 4:41

score 67 · Answer 2 · 2026-04-09 15:24:50

67

Views

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

Published on 09 Apr 2026 - 15:24

score 186 · Answer 3 · 2026-03-27 14:53:48

186

Views

how to check if a subgroup is maximal?

Published on 27 Mar 2026 - 14:53

score 403 · Answer 4 · 2026-03-25 04:41:09

403

Views

cardinality of a maximal subgroup of a $p$ group

Published on 25 Mar 2026 - 4:41

score 962 · Answer 5 · 2026-03-25 06:05:24

962

Views

All maximal independent sets of a matroid have the same cardinality

Published on 25 Mar 2026 - 6:05

score 205 · Answer 6 · 2026-04-10 18:21:29

205

Views

Why is $A_n$ maximal in $S_n$?

Published on 10 Apr 2026 - 18:21

score 93 · Answer 7 · 2026-03-25 06:04:20

93

Views

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

Published on 25 Mar 2026 - 6:04

score 1.3k · Answer 8 · 2026-04-11 00:10:17

1.3k

Views

Intersection of Maximal subgroups

Published on 11 Apr 2026 - 0:10

score 160 · Answer 9 · 2026-05-05 15:54:31

160

Views

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

Published on 05 May 2026 - 15:54

score 56 · Answer 10 · 2026-03-25 04:40:23

56

Views

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

Published on 25 Mar 2026 - 4:40

score 66 · Answer 11 · 2026-03-25 06:01:28

66

Views

Groups having no maximal cyclic subgroups of prime order

Published on 25 Mar 2026 - 6:01

score 225 · Answer 12 · 2026-03-25 04:41:00

225

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 25 Mar 2026 - 4:41

score 870 · Answer 13 · 2026-03-27 15:14:23

870

Views

Maximal & Maximal Normal Subgroups

Published on 27 Mar 2026 - 15:14

score 326 · Answer 14 · 2026-03-25 04:41:08

326

Views

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

Published on 25 Mar 2026 - 4:41

score 326 · Answer 15 · 2026-03-25 04:44:15

326

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 25 Mar 2026 - 4:44

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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