Question

Group is soluble if and only if quotient is abelian

score 188 · Answer 1 · 2026-03-25 17:39:36

188

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Group is soluble if and only if quotient is abelian

Published on 25 Mar 2026 - 17:39

score 304 · Answer 2 · 2019-04-19 15:32:57

304

Views

Hungerford Chapter 2 Section 2 Problem 2 WITHOUT using the structure theorem of finite abelian groups

Published on 19 Apr 2019 - 15:32

score 50 · Answer 3 · 2019-04-20 08:19:57

50

Views

Product of elements from Direct summand in the direct sum abelian group

Published on 20 Apr 2019 - 8:19

score 428 · Answer 4 · 2026-03-25 23:42:45

428

Views

Direct sum of $n$ (infinite) cyclic groups isomorphic to direct sum of $n$ copies of $\mathbb{Z}$?

Published on 25 Mar 2026 - 23:42

score 312 · Answer 5 · 2019-04-21 18:44:52

312

Views

Number of generators of subgroup

Published on 21 Apr 2019 - 18:44

score 416 · Answer 6 · 2026-03-26 04:08:58

416

Views

Enough injectives in the category of torsion abelian groups

Published on 26 Mar 2026 - 4:08

score 88 · Answer 7 · 2019-04-22 03:29:32

88

Views

Suppose that $H_1/H_2$ is Abelian. Show that $H_1 N / H_2 N$ is Abelian.

Published on 22 Apr 2019 - 3:29

score 105 · Answer 8 · 2019-04-23 03:57:21

105

Views

Let $S=\{x~|~x\in G$ and $x^2 \in H\}$. Show that $S$ is a subgroup of $G$ for $H<G$, $G$ abelian.

Published on 23 Apr 2019 - 3:57

score 452 · Answer 9 · 2019-04-23 05:23:42

452

Views

Number of subgroups of an abelian p-group

Published on 23 Apr 2019 - 5:23

score 569 · Answer 10 · 2019-04-23 08:12:34

569

Views

How do basic results in representation theory change going to positive characteristic fields and/or not algebraically closed?

Published on 23 Apr 2019 - 8:12

score 10.6k · Answer 11 · 2019-04-24 00:00:54

10.6k

Views

Does every subgroup of an abelian group have to be abelian?

Published on 24 Apr 2019 - 0:00

score 507 · Answer 12 · 2019-04-24 07:30:43

507

Views

Normal group of product of abelian and non-abelian simple groups

Published on 24 Apr 2019 - 7:30

score 143 · Answer 13 · 2019-04-24 14:16:24

143

Views

Example of a bilinear form of abelian groups

Published on 24 Apr 2019 - 14:16

score 191 · Answer 14 · 2019-04-24 15:15:50

191

Views

The set of bilinear forms is a right $(R \otimes R)$-module

Published on 24 Apr 2019 - 15:15

score 158 · Answer 15 · 2019-04-24 19:10:11

158

Views

What is this abelian group notation?

Published on 24 Apr 2019 - 19:10

List Question

Group is soluble if and only if quotient is abelian

Hungerford Chapter 2 Section 2 Problem 2 WITHOUT using the structure theorem of finite abelian groups

Product of elements from Direct summand in the direct sum abelian group

Direct sum of $n$ (infinite) cyclic groups isomorphic to direct sum of $n$ copies of $\mathbb{Z}$?

Number of generators of subgroup

Enough injectives in the category of torsion abelian groups

Suppose that $H_1/H_2$ is Abelian. Show that $H_1 N / H_2 N$ is Abelian.

Let $S=\{x~|~x\in G$ and $x^2 \in H\}$. Show that $S$ is a subgroup of $G$ for $H<G$, $G$ abelian.

Number of subgroups of an abelian p-group

How do basic results in representation theory change going to positive characteristic fields and/or not algebraically closed?

Does every subgroup of an abelian group have to be abelian?

Normal group of product of abelian and non-abelian simple groups

Example of a bilinear form of abelian groups

The set of bilinear forms is a right $(R \otimes R)$-module

What is this abelian group notation?

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