List questions from abelian-groups

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How to construct a homomorphism from an abelian group to $\mathbb{Q}$

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Let $G$ be a non-abelian group of order $10$. Prove that G has a trivial center.

Published on 09 May 2019 - 18:04

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$G$ is an abelian group, and a permutation $T$. Suppose that $x-T(x)\neq y-T(y)$ for all $x\neq y$. Show that $p(x)=x-T(x)$ is also a permutation

Published on 14 May 2019 - 13:03

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Inductive Proof of Group with Prime Decomposition is Isomorphic to Direct Product of Cyclic Groups

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Prove that every group of order 15 is abelian?

Published on 17 May 2019 - 9:17

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Why is $\mathbb{Z}\otimes Ag = Ag$, where Ag is an abelian group

Published on 19 May 2019 - 21:59

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ord$(h)|\max\{\text{ord}(g)|g\in G\}$ for all $h\in G$.

Published on 23 May 2019 - 8:29

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Internal direct sum of kernel of surjective homomorphism and cyclic subgroup

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Prove that there is no nonabelian simple group of order less than 60

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How to compute identity from symmetric difference?

Published on 26 May 2019 - 7:34

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In $U_{24}$, find a smallest positive integer $n$ such that $[7]^n=[1]$

Published on 26 May 2019 - 11:22

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Presentation of abelian groups and classification.

Published on 25 Mar 2026 - 12:46

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Show that upper triangular matrices group is solvable

Published on 25 Mar 2026 - 4:35

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Abelian groups having no finite subgroup

Published on 25 Mar 2026 - 12:55

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Subgroups of the integers

How to construct a homomorphism from an abelian group to $\mathbb{Q}$

Let $G$ be a non-abelian group of order $10$. Prove that G has a trivial center.

$G$ is an abelian group, and a permutation $T$. Suppose that $x-T(x)\neq y-T(y)$ for all $x\neq y$. Show that $p(x)=x-T(x)$ is also a permutation

Inductive Proof of Group with Prime Decomposition is Isomorphic to Direct Product of Cyclic Groups

Prove that every group of order 15 is abelian?

Why is $\mathbb{Z}\otimes Ag = Ag$, where Ag is an abelian group

ord$(h)|\max\{\text{ord}(g)|g\in G\}$ for all $h\in G$.

Internal direct sum of kernel of surjective homomorphism and cyclic subgroup

Prove that there is no nonabelian simple group of order less than 60

How to compute identity from symmetric difference?

In $U_{24}$, find a smallest positive integer $n$ such that $[7]^n=[1]$

Presentation of abelian groups and classification.

Show that upper triangular matrices group is solvable

Abelian groups having no finite subgroup

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