Question

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

score 116 · Answer 1 · 2026-03-25 15:42:36

116

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

Published on 25 Mar 2026 - 15:42

score 93 · Answer 2 · 2026-03-25 15:42:34

93

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

Published on 25 Mar 2026 - 15:42

score 124 · Answer 3 · 2026-03-25 15:42:22

124

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

Published on 25 Mar 2026 - 15:42

score 113 · Answer 4 · 2026-03-25 15:40:07

113

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Maximal Subgroups of $S_n$ with a certain proprety

Published on 25 Mar 2026 - 15:40

score 119 · Answer 5 · 2026-04-25 20:28:45

119

Views

Finite group with prime index maximal subgroups

Published on 25 Apr 2026 - 20:28

score 158 · Answer 6 · 2026-03-25 15:47:27

158

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Isaacs Algebra : A Graduate Course definition for diagonal subgroup

Published on 25 Mar 2026 - 15:47

score 92 · Answer 7 · 2026-05-10 19:13:10

92

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Frattini subgroup in abelian group

Published on 10 May 2026 - 19:13

score 88 · Answer 8 · 2026-03-25 15:44:10

88

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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 25 Mar 2026 - 15:44

score 472 · Answer 9 · 2026-03-25 15:42:11

472

Views

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

Published on 25 Mar 2026 - 15:42

score 105 · Answer 10 · 2026-03-25 15:42:32

105

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 25 Mar 2026 - 15:42

score 388 · Answer 11 · 2026-03-25 15:44:10

388

Views

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

Published on 25 Mar 2026 - 15:44

score 201 · Answer 12 · 2026-05-10 18:04:09

201

Views

Frattini subgroup of $p$-group

Published on 10 May 2026 - 18:04

score 146 · Answer 13 · 2026-03-25 15:41:12

146

Views

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

Published on 25 Mar 2026 - 15:41

score 138 · Answer 14 · 2026-03-25 15:39:20

138

Views

Non-trivial automorphisms that fix maximal subgroups?

Published on 25 Mar 2026 - 15:39

score 599 · Answer 15 · 2026-03-25 15:42:31

599

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 25 Mar 2026 - 15:42

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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