Question

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

score 1k · Answer 1 · 2019-04-24 20:50:37

1k

Views

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

Published on 24 Apr 2019 - 20:50

score 240 · Answer 2 · 2019-04-24 22:25:31

240

Views

Find the amount of subgroups of order $3$ and $21$ in non-cyclic abelian group of order $63$

Published on 24 Apr 2019 - 22:25

score 286 · Answer 3 · 2019-04-25 00:10:01

286

Views

Can a nonabelian group $G$ have a normal abelian subgroup $H$ with $[G:H]=3$?

Published on 25 Apr 2019 - 0:10

score 358 · Answer 4 · 2019-04-26 07:49:51

358

Views

Are all index 2 subgroups of $(\mathbb{Z} /2\mathbb{Z})^n$ isomorphic to $(\mathbb{Z} /2\mathbb{Z})^{n-1}$

Published on 26 Apr 2019 - 7:49

score 46 · Answer 5 · 2019-04-30 09:01:54

46

Views

Let $f(z)=|z-1|/(|z|^p+1)^{1/p}$, is it true that $f(z.w) \le f(z)+f(w)$?

Published on 30 Apr 2019 - 9:01

score 214 · Answer 6 · 2019-04-30 20:42:41

214

Views

If $V$ is a vector space then $(V,+)$ is a characteristically simple abelian group

Published on 30 Apr 2019 - 20:42

score 29 · Answer 7 · 2019-05-02 06:27:37

29

Views

A divisibility property of the direct sum of abelian groups

Published on 02 May 2019 - 6:27

score 64 · Answer 8 · 2019-05-02 06:40:42

64

Views

What is the maximal order among elements in $\mathbb{Z}\times(\mathbb{Z}/10\Bbb{Z})/\langle(5,4)\rangle$?

Published on 02 May 2019 - 6:40

score 82 · Answer 9 · 2019-05-03 08:27:58

82

Views

additive order of any zero divisor in $Z_{p^2}$ is p, is it true?

Published on 03 May 2019 - 8:27

score 296 · Answer 10 · 2026-03-25 12:53:46

296

Views

Why not $\mathbb{Q}$ and $\mathbb{Q}\times \mathbb{Q}\cong \mathbb{Q}^2$ not isomorphic as additive groups?

Published on 25 Mar 2026 - 12:53

score 72 · Answer 11 · 2026-03-25 22:01:47

72

Views

Groups, subgroups and quotient groups

Published on 25 Mar 2026 - 22:01

score 2.9k · Answer 12 · 2019-05-04 21:03:02

2.9k

Views

If every nonidentity element in a group is of order $2$, the group is abelian

Published on 04 May 2019 - 21:03

score 48 · Answer 13 · 2026-03-20 01:03:22

48

Views

Determining the Cyclic Decomposition of a Finitely Generated Abelian Group given a set of relations.

Published on 20 Mar 2026 - 1:03

score 36 · Answer 14 · 2019-05-06 19:04:10

36

Views

Cardinality of an intersection of two submodules.

Published on 06 May 2019 - 19:04

score 66 · Answer 15 · 2026-03-25 06:27:18

66

Views

Injection of $\mathbb{Z}$ into a p-adically complete abelian group

Published on 25 Mar 2026 - 6:27

List Question

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

Find the amount of subgroups of order $3$ and $21$ in non-cyclic abelian group of order $63$

Can a nonabelian group $G$ have a normal abelian subgroup $H$ with $[G:H]=3$?

Are all index 2 subgroups of $(\mathbb{Z} /2\mathbb{Z})^n$ isomorphic to $(\mathbb{Z} /2\mathbb{Z})^{n-1}$

Let $f(z)=|z-1|/(|z|^p+1)^{1/p}$, is it true that $f(z.w) \le f(z)+f(w)$?

If $V$ is a vector space then $(V,+)$ is a characteristically simple abelian group

A divisibility property of the direct sum of abelian groups

What is the maximal order among elements in $\mathbb{Z}\times(\mathbb{Z}/10\Bbb{Z})/\langle(5,4)\rangle$?

additive order of any zero divisor in $Z_{p^2}$ is p, is it true?

Why not $\mathbb{Q}$ and $\mathbb{Q}\times \mathbb{Q}\cong \mathbb{Q}^2$ not isomorphic as additive groups?

Groups, subgroups and quotient groups

If every nonidentity element in a group is of order $2$, the group is abelian

Determining the Cyclic Decomposition of a Finitely Generated Abelian Group given a set of relations.

Cardinality of an intersection of two submodules.

Injection of $\mathbb{Z}$ into a p-adically complete abelian group

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