Question

Proof about existence of subgroups in finite abelian group

score 638 · Answer 1 · 2014-06-03 16:11:17

638

Views

Proof about existence of subgroups in finite abelian group

Published on 03 Jun 2014 - 16:11

score 2.3k · Answer 2 · 2014-06-04 03:15:28

2.3k

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Free groups vs. free abelian groups

Published on 04 Jun 2014 - 3:15

score 242 · Answer 3 · 2014-06-04 18:00:54

242

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Self-duality of the subgroup lattice of finite abelian groups

Published on 04 Jun 2014 - 18:00

score 109 · Answer 4 · 2014-06-05 12:27:37

109

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What we know about $\mathbb{Q}/\mathbb{Z}$ as a group?

Published on 05 Jun 2014 - 12:27

score 305 · Answer 5 · 2014-06-06 01:35:08

305

Views

The factor group $\mathbb{R}^{*}/\{-1,1\}$ is isomorphic to $\mathbb{Z}_{2}$. True or False.

Published on 06 Jun 2014 - 1:35

score 95 · Answer 6 · 2014-06-07 11:57:28

95

Views

$\operatorname{Hom}(G,\Bbb C\setminus \{0\})$ non- isomorphic to $\operatorname{Hom}(G, \Bbb T)$?

Published on 07 Jun 2014 - 11:57

score 208 · Answer 7 · 2014-06-07 12:17:25

208

Views

Let $G$ be a group and $a,b,c \in G$. Given that $abc$ and $cba$ are conjugated, prove that $G$ is abelian.

Published on 07 Jun 2014 - 12:17

score 597 · Answer 8 · 2014-06-08 08:32:59

597

Views

How to prove that $\mathbb Z/p$ is not a direct summand of any direct sum of copies of $\mathbb Z/n$?

Published on 08 Jun 2014 - 8:32

score 59 · Answer 9 · 2014-06-08 22:04:07

59

Views

Show that, given an element $\bar{x}\in\mathbb{Q}/\mathbb{Z}$, there is an integer $n \ge 1$ such that $n\bar{x} = 0$.

Published on 08 Jun 2014 - 22:04

score 174 · Answer 10 · 2014-06-09 12:54:11

174

Views

A finite $\mathbb{Z}$-module whose submodules are totally ordered by inclusion.

Published on 09 Jun 2014 - 12:54

score 673 · Answer 11 · 2014-06-10 00:58:53

673

Views

$n$th power map is an automorphism implies abelian group?

Published on 10 Jun 2014 - 0:58

score 449 · Answer 12 · 2014-06-15 00:01:32

449

Views

Quotient group $\mathbb Z^n/\ \text{im}(A)$

Published on 15 Jun 2014 - 0:01

score 79 · Answer 13 · 2026-03-28 06:40:27

79

Views

What can I say about the quotient group?

Published on 28 Mar 2026 - 6:40

score 57 · Answer 14 · 2014-06-25 12:51:58

57

Views

maximal and minimal subgroups of torsion abelian groups

Published on 25 Jun 2014 - 12:51

score 57 · Answer 15 · 2014-06-25 16:41:03

57

Views

A group with bounded element orders and its minimal and maximal subgroups.

Published on 25 Jun 2014 - 16:41

List Question

Proof about existence of subgroups in finite abelian group

Free groups vs. free abelian groups

Self-duality of the subgroup lattice of finite abelian groups

What we know about $\mathbb{Q}/\mathbb{Z}$ as a group?

The factor group $\mathbb{R}^{*}/\{-1,1\}$ is isomorphic to $\mathbb{Z}_{2}$. True or False.

$\operatorname{Hom}(G,\Bbb C\setminus \{0\})$ non- isomorphic to $\operatorname{Hom}(G, \Bbb T)$?

Let $G$ be a group and $a,b,c \in G$. Given that $abc$ and $cba$ are conjugated, prove that $G$ is abelian.

How to prove that $\mathbb Z/p$ is not a direct summand of any direct sum of copies of $\mathbb Z/n$?

Show that, given an element $\bar{x}\in\mathbb{Q}/\mathbb{Z}$, there is an integer $n \ge 1$ such that $n\bar{x} = 0$.

A finite $\mathbb{Z}$-module whose submodules are totally ordered by inclusion.

$n$th power map is an automorphism implies abelian group?

Quotient group $\mathbb Z^n/\ \text{im}(A)$

What can I say about the quotient group?

maximal and minimal subgroups of torsion abelian groups

A group with bounded element orders and its minimal and maximal subgroups.

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