Question

Decomposition of characters of infinite product of abelian groups

score 112 · Answer 1 · 2020-01-21 11:11:17

112

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Decomposition of characters of infinite product of abelian groups

Published on 21 Jan 2020 - 11:11

score 85 · Answer 2 · 2026-03-27 21:35:45

85

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Prove that a group of order 45 is necessarily abelian by Sylows' Theorems

Published on 27 Mar 2026 - 21:35

score 382 · Answer 3 · 2020-01-25 07:05:00

382

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Let $(G,)$ be a group with $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5\forall a,b∈G$. Show that $(G,)$ is abelian.

Published on 25 Jan 2020 - 7:05

score 607 · Answer 4 · 2020-01-25 08:46:29

607

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Counting the number of particular subgroups of a finite abelian group

Published on 25 Jan 2020 - 8:46

score 121 · Answer 5 · 2020-01-25 15:18:52

121

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A group $(G,\cdot)$ where every element except $e$ is of order $p$

Published on 25 Jan 2020 - 15:18

score 83 · Answer 6 · 2026-03-26 06:21:20

83

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If we restrict the character $\chi:G\to S_{o(\chi)}$, then is this map surjective?

Published on 26 Mar 2026 - 6:21

score 100 · Answer 7 · 2026-03-27 00:09:44

100

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Torsion in abelian groups

Published on 27 Mar 2026 - 0:09

score 91 · Answer 8 · 2026-03-29 10:18:19

91

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Do these results also hold for automorphisms?

Published on 29 Mar 2026 - 10:18

score 504 · Answer 9 · 2020-01-26 02:44:59

504

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Ring homomorphisms form an abelian group

Published on 26 Jan 2020 - 2:44

score 159 · Answer 10 · 2020-01-27 10:58:18

159

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Which axioms fails for this ordered pairs to be a vector space?

Published on 27 Jan 2020 - 10:58

score 185 · Answer 11 · 2020-01-28 15:38:40

185

Views

Simple $G$-module where $G$ is commutative

Published on 28 Jan 2020 - 15:38

score 150 · Answer 12 · 2020-01-31 18:53:09

150

Views

Every abelian group admits a unique maximal divisible subgroup

Published on 31 Jan 2020 - 18:53

score 489 · Answer 13 · 2026-03-29 21:56:59

489

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If $G$ is an abelian group, let $H_p$ be the set of all $x \in G$ whose order is a power of $p$

Published on 29 Mar 2026 - 21:56

score 1.8k · Answer 14 · 2020-02-02 19:09:56

1.8k

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Let $G$ be an abelian group with identity $e$. Let $H=\left\{g\in G\mid g^2=e\right\}$. Show that $H\le G$.

Published on 02 Feb 2020 - 19:09

score 72 · Answer 15 · 2026-03-27 19:32:35

72

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A subring of $\mathbb{C}$ having $\mathbb{Z}$ as a direct summand as additive $\mathbb{Z}$-modules

Published on 27 Mar 2026 - 19:32

List Question

Decomposition of characters of infinite product of abelian groups

Prove that a group of order 45 is necessarily abelian by Sylows' Theorems

Let $(G,)$ be a group with $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5\forall a,b∈G$. Show that $(G,)$ is abelian.

Counting the number of particular subgroups of a finite abelian group

A group $(G,\cdot)$ where every element except $e$ is of order $p$

If we restrict the character $\chi:G\to S_{o(\chi)}$, then is this map surjective?

Torsion in abelian groups

Do these results also hold for automorphisms?

Ring homomorphisms form an abelian group

Which axioms fails for this ordered pairs to be a vector space?

Simple $G$-module where $G$ is commutative

Every abelian group admits a unique maximal divisible subgroup

If $G$ is an abelian group, let $H_p$ be the set of all $x \in G$ whose order is a power of $p$

Let $G$ be an abelian group with identity $e$. Let $H=\left\{g\in G\mid g^2=e\right\}$. Show that $H\le G$.

A subring of $\mathbb{C}$ having $\mathbb{Z}$ as a direct summand as additive $\mathbb{Z}$-modules

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