List questions from abelian-groups

Published on 11 Aug 2014 - 10:39

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If every element of $H$ and $G/H$ is a square, then prove that so is every element of $G$.

Published on 11 Aug 2014 - 15:27

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A sequence of subsets of $\Bbb Z$ not containing nontrivial subgroups

Published on 25 Mar 2026 - 14:27

491

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Does the following binary operation form a group on a set with 3 elements? (multiple identities?)

Published on 17 Aug 2014 - 9:33

813

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When is a non-trivial homomorphism injective?

Published on 17 Aug 2014 - 15:43

109

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Abelian group and morphism equivalent statement

Published on 17 Aug 2014 - 19:30

377

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Rational group algebras and maximal orders

Published on 25 Mar 2026 - 7:42

136

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An epimorphism from $\mathbb Z⊕\mathbb Z⊕\cdots$ to $\mathbb Q$

Published on 20 Aug 2014 - 15:08

436

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Exercise on characterization of free abelian groups

Published on 22 Aug 2014 - 18:07

64

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divisible subgroup without axiom of choice

Published on 27 Aug 2014 - 10:28

94

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From Automorphism to abelian ness ... in a finite group

Published on 31 Aug 2014 - 7:21

172

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$G$ is torsion-free $[G:Z(G)]$ is finite $\implies$ $G$ is abelian ?

Published on 31 Aug 2014 - 8:21

220

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Why does existence of abelian tower not imply solvability?

Published on 25 Mar 2026 - 14:22

135

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When an Abelian group is cyclic

Published on 07 Sep 2014 - 11:22

395

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$\mathbb{R}$ is not a direct sum of its subgroups

Published on 10 Sep 2014 - 15:19

List Question

Tensor product of $\mathbb{R}^d$ and $\mathbb{R}^s$ as abelian groups

If every element of $H$ and $G/H$ is a square, then prove that so is every element of $G$.

A sequence of subsets of $\Bbb Z$ not containing nontrivial subgroups

Does the following binary operation form a group on a set with 3 elements? (multiple identities?)

When is a non-trivial homomorphism injective?

Abelian group and morphism equivalent statement

Rational group algebras and maximal orders

An epimorphism from $\mathbb Z⊕\mathbb Z⊕\cdots$ to $\mathbb Q$

Exercise on characterization of free abelian groups

divisible subgroup without axiom of choice

From Automorphism to abelian ness ... in a finite group

$G$ is torsion-free $[G:Z(G)]$ is finite $\implies$ $G$ is abelian ?

Why does existence of abelian tower not imply solvability?

When an Abelian group is cyclic

$\mathbb{R}$ is not a direct sum of its subgroups

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