Question

What are the maximal subgroups of a finite abelian group in terms of characters?

score 115 · Answer 1 · 2021-04-29 12:36:16

115

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What are the maximal subgroups of a finite abelian group in terms of characters?

Published on 29 Apr 2021 - 12:36

score 92 · Answer 2 · 2021-06-15 15:36:12

92

Views

Maximal subgroup $G$ of $(\mathbb{R},+)$ w.r.t. the property that $1\not\in G$ contains a unique prime number

Published on 15 Jun 2021 - 15:36

score 123 · Answer 3 · 2021-06-19 02:53:41

123

Views

Let $G$ be a $p$-group. If every two maximal subgroups of $G$ are conjugated, then $G$ is cyclic

Published on 19 Jun 2021 - 2:53

score 112 · Answer 4 · 2021-08-15 17:04:04

112

Views

Maximal Subgroups of $S_n$ with a certain proprety

Published on 15 Aug 2021 - 17:04

score 104 · Answer 5 · 2026-03-24 23:02:46

104

Views

Finite group with prime index maximal subgroups

Published on 24 Mar 2026 - 23:02

score 157 · Answer 6 · 2021-08-31 21:24:39

157

Views

Isaacs Algebra : A Graduate Course definition for diagonal subgroup

Published on 31 Aug 2021 - 21:24

score 91 · Answer 7 · 2026-03-25 07:41:44

91

Views

Frattini subgroup in abelian group

Published on 25 Mar 2026 - 7:41

score 87 · Answer 8 · 2021-09-17 00:10:10

87

Views

Let $H\leq G$ where $H$ is max simple. Prove either $G$ is simple or there exists a minimal normal subgroup $N$ of $G$ such that $G/N$ is simple.

Published on 17 Sep 2021 - 0:10

score 471 · Answer 9 · 2021-09-18 19:59:26

471

Views

Show that $S_n$ is a maximal subgroup of $S_{n+1}$.

Published on 18 Sep 2021 - 19:59

score 104 · Answer 10 · 2021-10-05 17:51:35

104

Views

Let $G$ be a group and $M$ be a maximal abelian subgroup of $G$. Prove $C_M(g)\lneq M$ for every $g\in G-M$.

Published on 05 Oct 2021 - 17:51

score 387 · Answer 11 · 2021-11-01 22:18:22

387

Views

Why must we use Zorn's Lemma to prove every subgroup of $G$ is contained in a maximal subgroup of $G$?

Published on 01 Nov 2021 - 22:18

score 200 · Answer 12 · 2026-03-25 09:26:54

200

Views

Frattini subgroup of $p$-group

Published on 25 Mar 2026 - 9:26

score 145 · Answer 13 · 2021-12-20 16:33:14

145

Views

About non existence of maximal subgroup in additive group $\mathbb{Q}$

Published on 20 Dec 2021 - 16:33

score 137 · Answer 14 · 2021-12-20 20:57:40

137

Views

Non-trivial automorphisms that fix maximal subgroups?

Published on 20 Dec 2021 - 20:57

score 598 · Answer 15 · 2021-12-20 22:28:03

598

Views

Let $G$ be a finite $p$-group, where $p$ is prime. Show that if $G$ is not cyclic, then $G$ has at least $p+1$ maximal subgroups.

Published on 20 Dec 2021 - 22:28

List Question

What are the maximal subgroups of a finite abelian group in terms of characters?

Maximal subgroup $G$ of $(\mathbb{R},+)$ w.r.t. the property that $1\not\in G$ contains a unique prime number

Let $G$ be a $p$-group. If every two maximal subgroups of $G$ are conjugated, then $G$ is cyclic

Maximal Subgroups of $S_n$ with a certain proprety

Finite group with prime index maximal subgroups

Isaacs Algebra : A Graduate Course definition for diagonal subgroup

Frattini subgroup in abelian group

Let $H\leq G$ where $H$ is max simple. Prove either $G$ is simple or there exists a minimal normal subgroup $N$ of $G$ such that $G/N$ is simple.

Show that $S_n$ is a maximal subgroup of $S_{n+1}$.

Let $G$ be a group and $M$ be a maximal abelian subgroup of $G$. Prove $C_M(g)\lneq M$ for every $g\in G-M$.

Why must we use Zorn's Lemma to prove every subgroup of $G$ is contained in a maximal subgroup of $G$?

Frattini subgroup of $p$-group

About non existence of maximal subgroup in additive group $\mathbb{Q}$

Non-trivial automorphisms that fix maximal subgroups?

Let $G$ be a finite $p$-group, where $p$ is prime. Show that if $G$ is not cyclic, then $G$ has at least $p+1$ maximal subgroups.

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