List questions from abelian-groups

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$G$ abelian when $Z(G)$ is a proper subset of $G$?

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Invariant factor decomposition of quotient group of two subgroups of $\mathbb{Z}^n$.

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Computing Pontryagin Duals

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Determine the rank and the elementary divisors of each of the following groups.

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56

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existence of subgroups of finite abelian groups

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Theorem of structure for abelian groups

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In the category of abelian groups the coequalizer $\text{Coker}(f, 0)$, $f: A \to B$ is simply $B/f(A)$.

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Commutator subgroup and simple groups

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Are there any interesting examples of functions on Abelian groups that are not homomorphisms?

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Basic problems on Group Theory

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Relation between profinite abelian groups and $\hat{\Bbb{Z}}$ modules

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256

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How does abelianization work in defining homology?

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Problem on internal and external direct product?

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Show that the group $\mathbb Z_{45}$ has exactly one subgroup of order $3$ and construct it.

Published on 24 Mar 2026 - 20:32

List Question

How to construct a group whose "size" grows between polynomially and exponentially.

$G$ abelian when $Z(G)$ is a proper subset of $G$?

Invariant factor decomposition of quotient group of two subgroups of $\mathbb{Z}^n$.

Computing Pontryagin Duals

Determine the rank and the elementary divisors of each of the following groups.

existence of subgroups of finite abelian groups

Theorem of structure for abelian groups

In the category of abelian groups the coequalizer $\text{Coker}(f, 0)$, $f: A \to B$ is simply $B/f(A)$.

Commutator subgroup and simple groups

Are there any interesting examples of functions on Abelian groups that are not homomorphisms?

Basic problems on Group Theory

Relation between profinite abelian groups and $\hat{\Bbb{Z}}$ modules

How does abelianization work in defining homology?

Problem on internal and external direct product?

Show that the group $\mathbb Z_{45}$ has exactly one subgroup of order $3$ and construct it.

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