Question

Is it true that $G\cong\bigoplus_{\alpha\in A}\langle g_\alpha\rangle$ implies $G=\langle g_{\alpha}\mid \alpha\in A\rangle$?

score 39 · Answer 1 · 2016-11-23 17:40:39

39

Views

Is it true that $G\cong\bigoplus_{\alpha\in A}\langle g_\alpha\rangle$ implies $G=\langle g_{\alpha}\mid \alpha\in A\rangle$?

Published on 23 Nov 2016 - 17:40

score 337 · Answer 2 · 2016-12-14 15:33:12

337

Views

Free abelian groups and free groups

Published on 14 Dec 2016 - 15:33

score 180 · Answer 3 · 2017-01-16 01:38:32

180

Views

Primary Decomposition of group $G=\mathbb{Z}^{3}/N$ where $N\leq G$

Published on 16 Jan 2017 - 1:38

score 341 · Answer 4 · 2017-01-16 22:06:42

341

Views

Basis for free Abelian group $A_{n}$ of rank $n$

Published on 16 Jan 2017 - 22:06

score 193 · Answer 5 · 2017-01-29 05:12:23

193

Views

Matrix obtained by sequence of elementary transformations is equal to the original coordinate matrix multiplied by some matrices in $GL(n,\mathbb{Z})$

Published on 29 Jan 2017 - 5:12

score 507 · Answer 6 · 2017-01-30 00:58:55

507

Views

$X$ is a basis for free abelian group $A_{n}$ if and only if $\det (M) = \pm 1$

Published on 30 Jan 2017 - 0:58

score 684 · Answer 7 · 2017-02-03 05:36:01

684

Views

Want to prove $Aut(A_{n})\simeq GL(n, \mathbb{Z})$ where $A_{n}$ is a free abelian group of rank $n$

Published on 03 Feb 2017 - 5:36

score 754 · Answer 8 · 2017-02-06 04:01:54

754

Views

Prove that a free abelian group $A_{n}$ is finitely generated if and only if its rank $n$ is finite

Published on 06 Feb 2017 - 4:01

score 328 · Answer 9 · 2017-03-28 03:21:26

328

Views

Grothendieck Group - why not the free abelian group?

Published on 28 Mar 2017 - 3:21

score 167 · Answer 10 · 2017-03-28 07:42:18

167

Views

Lang's Theorem 7.3 wording, what does he mean?

Published on 28 Mar 2017 - 7:42

score 89 · Answer 11 · 2023-02-14 19:39:14

89

Views

Obtaining an isomorphism from a surjective homomorphism between abelian groups

Published on 14 Feb 2023 - 19:39

score 28 · Answer 12 · 2023-03-13 10:30:42

28

Views

Dual group of the torus

Published on 13 Mar 2023 - 10:30

score 49 · Answer 13 · 2023-04-11 22:48:17

49

Views

Construction of Free abelian groups on Massey Book

Published on 11 Apr 2023 - 22:48

score 120 · Answer 14 · 2023-05-02 12:27:02

120

Views

Proof verification of decomposition of abelian group into torsion and free groups

Published on 02 May 2023 - 12:27

score 50 · Answer 15 · 2023-05-10 08:01:42

50

Views

Given a non-singular rational matrix $Q \in \mathbb Q^{n\times n}$, what is $Q(\mathbb Z^{n}) \cap \mathbb Z^{n}$?

Published on 10 May 2023 - 8:01

List Question

Is it true that $G\cong\bigoplus_{\alpha\in A}\langle g_\alpha\rangle$ implies $G=\langle g_{\alpha}\mid \alpha\in A\rangle$?

Free abelian groups and free groups

Primary Decomposition of group $G=\mathbb{Z}^{3}/N$ where $N\leq G$

Basis for free Abelian group $A_{n}$ of rank $n$

Matrix obtained by sequence of elementary transformations is equal to the original coordinate matrix multiplied by some matrices in $GL(n,\mathbb{Z})$

$X$ is a basis for free abelian group $A_{n}$ if and only if $\det (M) = \pm 1$

Want to prove $Aut(A_{n})\simeq GL(n, \mathbb{Z})$ where $A_{n}$ is a free abelian group of rank $n$

Prove that a free abelian group $A_{n}$ is finitely generated if and only if its rank $n$ is finite

Grothendieck Group - why not the free abelian group?

Lang's Theorem 7.3 wording, what does he mean?

Obtaining an isomorphism from a surjective homomorphism between abelian groups

Dual group of the torus

Construction of Free abelian groups on Massey Book

Proof verification of decomposition of abelian group into torsion and free groups

Given a non-singular rational matrix $Q \in \mathbb Q^{n\times n}$, what is $Q(\mathbb Z^{n}) \cap \mathbb Z^{n}$?

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