List questions from abelian-groups

Published on 19 Mar 2026 - 10:51

121

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Showing $\{g \in G: g^n=1\}$ is a cyclic subgroup of cyclic $G$ of order $n$ for $|G|=nk, k\in\Bbb N$.

Published on 31 Aug 2019 - 18:41

44

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Is it true that $\oplus_G H \cong \mathbb{Z}[G] \otimes_{\mathbb{Z}} H$ as $\mathbb{Z}[G]$ module?

Published on 01 Sep 2019 - 8:50

714

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If $G=HK$, $H,K$ are normal in $G$, and $H\cap K=\{e\}$ then $G$ is abelian

Published on 01 Sep 2019 - 13:32

61

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class of abelian groups

Published on 26 Mar 2026 - 4:29

101

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Pluennecke inequality for Lebesgue measure?

Published on 06 Sep 2019 - 16:18

160

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Proving that the following subset of $\mathbb{Z}$ is the subgroup generated by its minimum

Published on 26 Mar 2026 - 3:12

64

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Existence of limits of group elements

Published on 08 Sep 2019 - 23:13

750

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Why is the empty set assigned the trivial group in the definition of a pre-sheaf?

Published on 09 Sep 2019 - 19:49

365

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Prove commutative subgroup

Published on 09 Sep 2019 - 22:31

113

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Subgroup of multiples of $m$, $m$-torsion and $p$-subgroup of $\mathbb{Z}_n$

Published on 10 Sep 2019 - 21:18

1.5k

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Let $S$ is a semi-group such that $x^2y=y=yx^2$ for all $x,y$ in $S$. Is it a group and if yes, is it abelian?

Published on 25 Mar 2026 - 9:30

573

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The number of generators of an abelian group of order $p^n$ with $p$ a prime

Published on 12 Sep 2019 - 12:46

29

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Order of a sum of elements in an abelian group

Published on 12 Sep 2019 - 22:09

155

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Find the number of subgroups of order $25$ when $G=\Bbb{Z}_{360}\times\Bbb{Z}_{120}\times\Bbb{Z}_{75}\times\Bbb{Z}_{3}$

Published on 26 Mar 2026 - 13:02

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Reference for a result in Abelian Group Theory

Showing $\{g \in G: g^n=1\}$ is a cyclic subgroup of cyclic $G$ of order $n$ for $|G|=nk, k\in\Bbb N$.

Is it true that $\oplus_G H \cong \mathbb{Z}[G] \otimes_{\mathbb{Z}} H$ as $\mathbb{Z}[G]$ module?

If $G=HK$, $H,K$ are normal in $G$, and $H\cap K=\{e\}$ then $G$ is abelian

class of abelian groups

Pluennecke inequality for Lebesgue measure?

Proving that the following subset of $\mathbb{Z}$ is the subgroup generated by its minimum

Existence of limits of group elements

Why is the empty set assigned the trivial group in the definition of a pre-sheaf?

Prove commutative subgroup

Subgroup of multiples of $m$, $m$-torsion and $p$-subgroup of $\mathbb{Z}_n$

Let $S$ is a semi-group such that $x^2y=y=yx^2$ for all $x,y$ in $S$. Is it a group and if yes, is it abelian?

The number of generators of an abelian group of order $p^n$ with $p$ a prime

Order of a sum of elements in an abelian group

Find the number of subgroups of order $25$ when $G=\Bbb{Z}_{360}\times\Bbb{Z}_{120}\times\Bbb{Z}_{75}\times\Bbb{Z}_{3}$

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