List questions from abelian-groups

88

Views

Does exactness of $0 \to \Bbb Z^n \to G \to \Bbb Z^m \to 0$ imply $G$ is isomorphic to $\Bbb Z^{m+n}$?

Published on 26 Mar 2026 - 6:23

239

Views

Is a single element linearly independent in an abelian group?

Published on 17 Sep 2019 - 15:18

309

Views

Show that a group $G$ is abelian if $(gh)^3 = g^3h^3$, $(gh)^4 = g^4h^4$, and $(gh)^5 = g^5h^5$ for all $g$ and $h$ in $G$.

Published on 18 Sep 2019 - 1:24

1000

Views

group of order $p^n$

Published on 19 Sep 2019 - 5:06

68

Views

Let $(G, \cdot)$ be an abelian group, and $g, h\in G$ have orders $a$ and $b$ respectively. What can you say about $(gh)^{ax_0}$?

Published on 19 Sep 2019 - 17:14

156

Views

Universal property on direct sums of abelian groups, struggling with uniqueness

Published on 21 Sep 2019 - 18:41

1.7k

Views

Examples of non-abelian groups under addition

Published on 25 Mar 2026 - 20:18

2k

Views

Is every group the unit group of some ring?

Published on 24 Sep 2019 - 0:06

324

Views

Smith normal form and group representation

Published on 23 Feb 2026 - 5:58

283

Views

A group of order pq

Published on 25 Mar 2026 - 6:29

1.1k

Views

When will a group be Abelian?

Published on 26 Mar 2026 - 23:59

328

Views

Divisible hull of a subgroup of $\mathbb{Q}^n$

Published on 26 Sep 2019 - 23:18

80

Views

On the proof of $A=\bigcap_{p\in\Bbb{P}}[\Bbb{Z}_{(p)}\otimes A]$

Published on 26 Sep 2019 - 23:35

1.2k

Views

If $G$ is an abelian group and $H$ be any subgroup, then why is $G/H$ also a group?

Published on 28 Sep 2019 - 4:49

103

Views

Product of all elements in a finite, boolean group

Published on 30 Sep 2019 - 0:50

List Question

Does exactness of $0 \to \Bbb Z^n \to G \to \Bbb Z^m \to 0$ imply $G$ is isomorphic to $\Bbb Z^{m+n}$?

Is a single element linearly independent in an abelian group?

Show that a group $G$ is abelian if $(gh)^3 = g^3h^3$, $(gh)^4 = g^4h^4$, and $(gh)^5 = g^5h^5$ for all $g$ and $h$ in $G$.

group of order $p^n$

Let $(G, \cdot)$ be an abelian group, and $g, h\in G$ have orders $a$ and $b$ respectively. What can you say about $(gh)^{ax_0}$?

Universal property on direct sums of abelian groups, struggling with uniqueness

Examples of non-abelian groups under addition

Is every group the unit group of some ring?

Smith normal form and group representation

A group of order pq

When will a group be Abelian?

Divisible hull of a subgroup of $\mathbb{Q}^n$

On the proof of $A=\bigcap_{p\in\Bbb{P}}[\Bbb{Z}_{(p)}\otimes A]$

If $G$ is an abelian group and $H$ be any subgroup, then why is $G/H$ also a group?

Product of all elements in a finite, boolean group

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