List questions from abelian-groups

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Prove that if $G$ is a finite group, then the index of $Z(G)$ cannot be prime.

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Does a list of elements' orders in an abelian group determine the group?

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Product of all elements in finite Abelian group times random group element

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Torsion-free abelian groups, tensor product and $p$-adic integers

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Prove that every irreducible real representation of an abelian group is one or two dimensional.

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Cyclic quotient group of permutation group $\mathbb{S}_n$

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If $G = \mathbb{Z}_{p}^{*} $, show that $G$ is cyclic

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Homomorphisms Group Theory

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Are all abelian subgroups of symmetric groups generated by disjoint cycles?

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Is $|\{z\in\Bbb Z_3\times\Bbb Z_9: |z|=9\}|=18?$

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An exact sequence of abelian groups

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Coset Progression is Freiman Isomorphic to Bohr Set

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why splitting lemma fails for nonabelian groups?

Published on 28 Feb 2019 - 18:03

List Question

Proper $\Bbb Z$-submodules of $\Bbb Q$ are finitely generated or not?

Torsion-free Abelian Groups of Finite Rank and Free Groups (Fuchs) - Self study

Prove that if $G$ is a finite group, then the index of $Z(G)$ cannot be prime.

Does a list of elements' orders in an abelian group determine the group?

Product of all elements in finite Abelian group times random group element

Torsion-free abelian groups, tensor product and $p$-adic integers

Prove that every irreducible real representation of an abelian group is one or two dimensional.

Cyclic quotient group of permutation group $\mathbb{S}_n$

If $G = \mathbb{Z}_{p}^{*} $, show that $G$ is cyclic

Homomorphisms Group Theory

Are all abelian subgroups of symmetric groups generated by disjoint cycles?

Is $|\{z\in\Bbb Z_3\times\Bbb Z_9: |z|=9\}|=18?$

An exact sequence of abelian groups

Coset Progression is Freiman Isomorphic to Bohr Set

why splitting lemma fails for nonabelian groups?

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