Question

Direct product of groups and isomorphism

score 47 · Answer 1 · 2026-03-26 11:00:10

47

Views

Direct product of groups and isomorphism

Published on 26 Mar 2026 - 11:00

score 242 · Answer 2 · 2014-12-07 04:55:34

242

Views

$G/Z(G)$ is cyclic useful for proving groups abelian?

Published on 07 Dec 2014 - 4:55

score 162 · Answer 3 · 2014-12-07 14:36:19

162

Views

Computing the quotient group

Published on 07 Dec 2014 - 14:36

score 705 · Answer 4 · 2014-12-10 06:58:02

705

Views

Prove every subgroup S of a finitely generated abelian group G is itself finitely generated.

Published on 10 Dec 2014 - 6:58

score 384 · Answer 5 · 2014-12-10 08:22:15

384

Views

Is there a homomorphism from a full product of finite cyclic groups onto $\mathbb Z$?

Published on 10 Dec 2014 - 8:22

score 151 · Answer 6 · 2026-03-29 03:22:24

151

Views

A group in between the commutator subgroup and the original group must be normal

Published on 29 Mar 2026 - 3:22

score 82 · Answer 7 · 2026-03-25 16:03:57

82

Views

If $X$ is an Abelian group, then $\ker_X : \mathrm{Cong}(X) \rightarrow \mathrm{Sub}(X)$ is a bijection. Is there a partial converse?

Published on 25 Mar 2026 - 16:03

score 82 · Answer 8 · 2014-12-12 05:40:40

82

Views

$G$ is a finite abelian group and $m:=\max \{o(x):x \in G\}$ , then is it true that $o(x)|m , \forall x \in G$?

Published on 12 Dec 2014 - 5:40

score 1.4k · Answer 9 · 2014-12-12 11:45:56

1.4k

Views

Every element in a finite (abelian) group $G$ is an $n$'th power if $\,\gcd(n,|G|)=1$

Published on 12 Dec 2014 - 11:45

score 948 · Answer 10 · 2014-12-12 13:52:13

948

Views

Which of the following abelian groups are cyclic groups?

Published on 12 Dec 2014 - 13:52

score 6.3k · Answer 11 · 2014-12-13 03:47:51

6.3k

Views

Every inﬁnite abelian group has at least one element of inﬁnite order?

Published on 13 Dec 2014 - 3:47

score 6.7k · Answer 12 · 2026-03-29 03:11:01

6.7k

Views

Prove a quotient group is abelian

Published on 29 Mar 2026 - 3:11

score 544 · Answer 13 · 2014-12-14 00:08:15

544

Views

Understanding the definition of tensor product as a quotient of a free abelian group

Published on 14 Dec 2014 - 0:08

score 71 · Answer 14 · 2014-12-14 22:09:07

71

Views

Odd order n smaller than 27

Published on 14 Dec 2014 - 22:09

score 78 · Answer 15 · 2014-12-15 14:55:23

78

Views

For $G$ an abelian group and $H$ a subgroup, is $[G : H]$ the smallest positive integer $n$ such that $ng \in H$ for all $g \in G$?

Published on 15 Dec 2014 - 14:55

List Question

Direct product of groups and isomorphism

$G/Z(G)$ is cyclic useful for proving groups abelian?

Computing the quotient group

Prove every subgroup S of a finitely generated abelian group G is itself finitely generated.

Is there a homomorphism from a full product of finite cyclic groups onto $\mathbb Z$?

A group in between the commutator subgroup and the original group must be normal

If $X$ is an Abelian group, then $\ker_X : \mathrm{Cong}(X) \rightarrow \mathrm{Sub}(X)$ is a bijection. Is there a partial converse?

$G$ is a finite abelian group and $m:=\max \{o(x):x \in G\}$ , then is it true that $o(x)|m , \forall x \in G$?

Every element in a finite (abelian) group $G$ is an $n$'th power if $\,\gcd(n,|G|)=1$

Which of the following abelian groups are cyclic groups?

Every inﬁnite abelian group has at least one element of inﬁnite order?

Prove a quotient group is abelian

Understanding the definition of tensor product as a quotient of a free abelian group

Odd order n smaller than 27

For $G$ an abelian group and $H$ a subgroup, is $[G : H]$ the smallest positive integer $n$ such that $ng \in H$ for all $g \in G$?

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