List questions from abelian-groups

Published on 02 Mar 2019 - 10:56

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Proving Abelian Group Decomposition Uniqueness

Published on 03 Mar 2019 - 18:17

245

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Find invariant factors from elementary divisors of an abelian group of order 720

Published on 03 Mar 2019 - 22:00

519

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Let $G$ be Abelian. Then any subgroup of $G$ is normal. Does the converse hold?

Published on 06 Mar 2019 - 16:47

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finite abelian groups tensor product.

Published on 11 Mar 2019 - 18:15

118

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if $G$ is a divisible group then any subgroup of $G$ is also divisible

Published on 12 Mar 2019 - 4:06

281

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Group Homomorphisms into an Abelian Group

Published on 13 Mar 2019 - 6:26

236

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Associocommutativity

Published on 25 Mar 2026 - 1:31

68

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All the $m$th powers commute with each other and all the $n$th powers commute with each other, $m$ and $n$ relative prime, is abelian.

Published on 13 Mar 2019 - 15:27

52

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Modifying long exact sequences

Published on 25 Mar 2026 - 22:24

226

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Relationship between Archimedean and Divisible ordered groups

Published on 25 Mar 2026 - 11:29

97

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prove that for $G$ a multiplicative nonabelian group of order $pq$, where $p$ and $q$ are prime numbers, any proper subgroup of $G$ is abelian

Published on 14 Mar 2019 - 7:58

652

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G is a group and $(ab)^3=a^3b^3$ for all $a,b \in G$. Prove (or disprove with a counterexample) that if $(ab)^3=(ba)^3$, then $ab=ba$.

Published on 18 Mar 2019 - 0:42

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Find the isomorphism type

Published on 25 Mar 2026 - 9:32

242

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Why does $a^{m_1}=a^{m_2}$ imply $a^{m_1-m_2}=e$?

Published on 20 Mar 2019 - 16:46

List Question

Quotients of finitely generated abelian groups

Proving Abelian Group Decomposition Uniqueness

Find invariant factors from elementary divisors of an abelian group of order 720

Let $G$ be Abelian. Then any subgroup of $G$ is normal. Does the converse hold?

finite abelian groups tensor product.

if $G$ is a divisible group then any subgroup of $G$ is also divisible

Group Homomorphisms into an Abelian Group

Associocommutativity

All the $m$th powers commute with each other and all the $n$th powers commute with each other, $m$ and $n$ relative prime, is abelian.

Modifying long exact sequences

Relationship between Archimedean and Divisible ordered groups

prove that for $G$ a multiplicative nonabelian group of order $pq$, where $p$ and $q$ are prime numbers, any proper subgroup of $G$ is abelian

G is a group and $(ab)^3=a^3b^3$ for all $a,b \in G$. Prove (or disprove with a counterexample) that if $(ab)^3=(ba)^3$, then $ab=ba$.

Find the isomorphism type

Why does $a^{m_1}=a^{m_2}$ imply $a^{m_1-m_2}=e$?

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