List questions from group-homomorphism

Published on 25 Mar 2026 - 23:53

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How to prove that a given function is not a group homomorphism?

Published on 03 Apr 2017 - 7:00

340

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Intuitive meaning of the $N/C$ theorem

Published on 05 Apr 2017 - 9:24

772

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How to solve Fundamental Theorem of Homomorphisms problems

Published on 06 Apr 2017 - 18:15

532

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Conjugation by the transpose homomorphism

Published on 06 Apr 2017 - 21:54

48

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Calculate $Hom_{Grp}(\Bbb{Q},\Bbb{Z})$

Published on 07 Apr 2017 - 1:58

289

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isomorphism between some Permutation groups

Published on 07 Apr 2017 - 21:43

78

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Homomorphism Group From $S_3$ to $\Bbb Z_5 \setminus \{0\}$

Published on 30 Jan 2023 - 1:24

102

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homomorphisms from S3 to Z24

Published on 31 Jan 2023 - 13:39

122

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An exercise on a function $f$ satisfying $f(x+y)=f(x)+f(y)$

Published on 14 Mar 2026 - 13:01

203

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For a finite abelian $G$, $f: G\to G$ defined by $f(g)=g^2$ is an isomorphism iff $|G|$ is odd

Published on 03 Feb 2023 - 14:11

247

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Suppose we have a homomorphism $f:G\to\Bbb Z$ for a finite group $G$. Prove that $f(g)=0$ for all $g$ in $G$

Published on 05 Feb 2023 - 17:40

73

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Preimage of an Abelian/Cyclic tower is an Abelian/Cyclic tower

Published on 07 Feb 2023 - 23:47

348

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Analog of Cantor-Schroder-Bernstein theorem for surjective homomorphisms between groups?

Published on 09 Feb 2023 - 3:48

189

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Finding an example of a group with some properties

Published on 10 Feb 2023 - 14:21

List Question

Mapping (in/sur/bi-jective) between a group to its (normal subgroup, quotient group)

How to prove that a given function is not a group homomorphism?

Intuitive meaning of the $N/C$ theorem

How to solve Fundamental Theorem of Homomorphisms problems

Conjugation by the transpose homomorphism

Calculate $Hom_{Grp}(\Bbb{Q},\Bbb{Z})$

isomorphism between some Permutation groups

Homomorphism Group From $S_3$ to $\Bbb Z_5 \setminus \{0\}$

homomorphisms from S3 to Z24

An exercise on a function $f$ satisfying $f(x+y)=f(x)+f(y)$

For a finite abelian $G$, $f: G\to G$ defined by $f(g)=g^2$ is an isomorphism iff $|G|$ is odd

Suppose we have a homomorphism $f:G\to\Bbb Z$ for a finite group $G$. Prove that $f(g)=0$ for all $g$ in $G$

Preimage of an Abelian/Cyclic tower is an Abelian/Cyclic tower

Analog of Cantor-Schroder-Bernstein theorem for surjective homomorphisms between groups?

Finding an example of a group with some properties

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