Question

Finitely generated abelian groups isomorphism

score 185 · Answer 1 · 2014-12-31 14:10:16

185

Views

Finitely generated abelian groups isomorphism

Published on 31 Dec 2014 - 14:10

score 50 · Answer 2 · 2014-12-31 17:53:28

50

Views

If $A$ is an Abelian group and $B < A$, $ A \simeq B \simeq \mathbb Z^n$ for some natural $n$. Prove that $mA \subset B $ for some $m$.

Published on 31 Dec 2014 - 17:53

score 110 · Answer 3 · 2014-12-31 18:34:49

110

Views

Prove that if $A,B$ are finite Abelian groups and for every $n$ they have the same amount of elements of order $n$, then $A \simeq B$

Published on 31 Dec 2014 - 18:34

score 205 · Answer 4 · 2026-03-29 13:52:25

205

Views

$O(G)=p^2 $, $p$ prime, $|Z(G)|>1$; prove $G$ abelian

Published on 29 Mar 2026 - 13:52

score 592 · Answer 5 · 2015-01-01 18:10:54

592

Views

Let $G$ to be abelian group and $|G|=mn$ when $(m,n)=1$. $G_m=\{g\mid g^m=e\}$,$G_n=\{g\mid g^n=e\}$, prove isomorphism

Published on 01 Jan 2015 - 18:10

score 76 · Answer 6 · 2015-01-01 23:37:01

76

Views

What does $d_{n+1}\circ{d_{n}}=0$ mean in the definition of a chain complex?

Published on 01 Jan 2015 - 23:37

score 49 · Answer 7 · 2026-03-26 17:27:46

49

Views

(shorter) exact sequences

Published on 26 Mar 2026 - 17:27

score 92 · Answer 8 · 2026-03-26 17:33:59

92

Views

Isomorphism between free abelian groups that fit into a short exact sequence

Published on 26 Mar 2026 - 17:33

score 653 · Answer 9 · 2026-03-28 22:47:26

653

Views

$Q$ is an injective object in an abelian category iff $\text{Hom}_C(\cdot, Q)$ is exact, the $\Rightarrow$ direction.

Published on 28 Mar 2026 - 22:47

score 35 · Answer 10 · 2026-03-29 04:48:08

35

Views

On systems of numeration and groups

Published on 29 Mar 2026 - 4:48

score 819 · Answer 11 · 2019-10-10 00:30:01

819

Views

If every proper subgroup of a nonabelian group is abelian, why must the group be generated by two elements?

Published on 10 Oct 2019 - 0:30

score 145 · Answer 12 · 2019-10-10 06:44:30

145

Views

Finite abelian groups of order 72 that have elements of order $4$?

Published on 10 Oct 2019 - 6:44

score 129 · Answer 13 · 2026-03-26 18:59:48

129

Views

Proving exact sequence of abelian groups splits

Published on 26 Mar 2026 - 18:59

score 68 · Answer 14 · 2026-03-27 01:34:12

68

Views

Does $\mathbb Z/p\mathbb Z$ a free abelian pro-p group?

Published on 27 Mar 2026 - 1:34

score 66 · Answer 15 · 2026-03-28 02:44:59

66

Views

On the proof that $(\Bbb{Q}\otimes A)\cap (\Bbb{Z}_p\otimes A)=\Bbb{Z}_{(p)}\otimes A$

Published on 28 Mar 2026 - 2:44

List Question

Finitely generated abelian groups isomorphism

If $A$ is an Abelian group and $B < A$, $ A \simeq B \simeq \mathbb Z^n$ for some natural $n$. Prove that $mA \subset B $ for some $m$.

Prove that if $A,B$ are finite Abelian groups and for every $n$ they have the same amount of elements of order $n$, then $A \simeq B$

$O(G)=p^2 $, $p$ prime, $|Z(G)|>1$; prove $G$ abelian

Let $G$ to be abelian group and $|G|=mn$ when $(m,n)=1$. $G_m=\{g\mid g^m=e\}$,$G_n=\{g\mid g^n=e\}$, prove isomorphism

What does $d_{n+1}\circ{d_{n}}=0$ mean in the definition of a chain complex?

(shorter) exact sequences

Isomorphism between free abelian groups that fit into a short exact sequence

$Q$ is an injective object in an abelian category iff $\text{Hom}_C(\cdot, Q)$ is exact, the $\Rightarrow$ direction.

On systems of numeration and groups

If every proper subgroup of a nonabelian group is abelian, why must the group be generated by two elements?

Finite abelian groups of order 72 that have elements of order $4$?

Proving exact sequence of abelian groups splits

Does $\mathbb Z/p\mathbb Z$ a free abelian pro-p group?

On the proof that $(\Bbb{Q}\otimes A)\cap (\Bbb{Z}_p\otimes A)=\Bbb{Z}_{(p)}\otimes A$

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