Question

For which abelian groups $G$ is there a short exact sequence $0 \rightarrow \mathbb{Z}/p^2 \rightarrow G \rightarrow \mathbb{Z}/p^2 \rightarrow 0$?

score 331 · Answer 1 · 2026-03-25 20:53:28

331

Views

For which abelian groups $G$ is there a short exact sequence $0 \rightarrow \mathbb{Z}/p^2 \rightarrow G \rightarrow \mathbb{Z}/p^2 \rightarrow 0$?

Published on 25 Mar 2026 - 20:53

score 107 · Answer 2 · 2026-03-25 04:36:31

107

Views

Abelian normal subgroups of A-groups

Published on 25 Mar 2026 - 4:36

score 210 · Answer 3 · 2018-12-29 03:47:34

210

Views

Representations and subgroups of the translation group

Published on 29 Dec 2018 - 3:47

score 99 · Answer 4 · 2018-12-29 05:14:05

99

Views

On a characterization of abelian groups $G$ based on special commutator relations ($\exists n\in\Bbb N$ s.t. $[x^n,y]=[x,y^{n+1}],\forall x,y \in G$).

Published on 29 Dec 2018 - 5:14

score 115 · Answer 5 · 2018-12-29 10:34:19

115

Views

Let $N$ be an Abelian normal subgroup of $G$, if $G/N$ is perfect, then also $G'$ is perfect.

Published on 29 Dec 2018 - 10:34

score 2.8k · Answer 6 · 2019-01-04 11:03:41

2.8k

Views

Classification of abelian groups of order 72, and subgroups of order 4

Published on 04 Jan 2019 - 11:03

score 57 · Answer 7 · 2019-01-04 16:02:57

57

Views

Is this true for about abelian generating sets?

Published on 04 Jan 2019 - 16:02

score 216 · Answer 8 · 2019-01-05 19:50:08

216

Views

Why does not generator of multiplicative group generate all the members of group?

Published on 05 Jan 2019 - 19:50

score 23 · Answer 9 · 2019-01-07 09:44:35

23

Views

How do you call groups formed as direct sums of cyclic groups?

Published on 07 Jan 2019 - 9:44

score 44 · Answer 10 · 2019-01-10 14:39:37

44

Views

Is there an algorithmic way to compute the quotient of two subgroups of $\mathbb Z^n$?

Published on 10 Jan 2019 - 14:39

score 294 · Answer 11 · 2019-01-11 17:33:51

294

Views

Are the groups $(\Bbb Q^2,+)$ and $(\Bbb Q,+)$ isomorphic?

Published on 11 Jan 2019 - 17:33

score 3.6k · Answer 12 · 2019-01-13 19:10:19

3.6k

Views

An abelian group $G$ of order $35$ with $g^{35}=e$ for all $g\in G$ is cyclic.

Published on 13 Jan 2019 - 19:10

score 218 · Answer 13 · 2019-01-14 13:55:39

218

Views

Find all non-isomorphic abelian groups s.t. $|G| \leq 30$ and $g^{12}=1, \, \forall g\in G$

Published on 14 Jan 2019 - 13:55

score 685 · Answer 14 · 2019-01-15 07:24:22

685

Views

How do we show that the set of module homomorphisms is a commutative group?

Published on 15 Jan 2019 - 7:24

score 334 · Answer 15 · 2019-01-15 17:17:18

334

Views

Proof for this identity in an abelian group

Published on 15 Jan 2019 - 17:17

List Question

For which abelian groups $G$ is there a short exact sequence $0 \rightarrow \mathbb{Z}/p^2 \rightarrow G \rightarrow \mathbb{Z}/p^2 \rightarrow 0$?

Abelian normal subgroups of A-groups

Representations and subgroups of the translation group

On a characterization of abelian groups $G$ based on special commutator relations ($\exists n\in\Bbb N$ s.t. $[x^n,y]=[x,y^{n+1}],\forall x,y \in G$).

Let $N$ be an Abelian normal subgroup of $G$, if $G/N$ is perfect, then also $G'$ is perfect.

Classification of abelian groups of order 72, and subgroups of order 4

Is this true for about abelian generating sets?

Why does not generator of multiplicative group generate all the members of group?

How do you call groups formed as direct sums of cyclic groups?

Is there an algorithmic way to compute the quotient of two subgroups of $\mathbb Z^n$?

Are the groups $(\Bbb Q^2,+)$ and $(\Bbb Q,+)$ isomorphic?

An abelian group $G$ of order $35$ with $g^{35}=e$ for all $g\in G$ is cyclic.

Find all non-isomorphic abelian groups s.t. $|G| \leq 30$ and $g^{12}=1, \, \forall g\in G$

How do we show that the set of module homomorphisms is a commutative group?

Proof for this identity in an abelian group

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