List questions from group-homomorphism

Published on 03 Oct 2019 - 20:34

1.2k

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Proving isomorphism on additive group $(\Bbb{Z}_4,+)$ and multiplicative group $(\Bbb{Z}_5^*, \times)$

Published on 06 Oct 2019 - 2:55

1.3k

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Is mapping generators to generators, and then extending, a well-defined homomorphism?

Published on 06 Oct 2019 - 19:15

137

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$H \subseteq G$. About the embedding(s?) of $\operatorname{Sym}(H)$ into $\operatorname{Sym}(G)$

Published on 08 Oct 2019 - 13:19

38

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Name of this homomorphism like mapping

Published on 25 Mar 2026 - 14:38

44

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How to simplify the Kernel of a homomorphism

Published on 11 Oct 2019 - 0:16

77

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At most one homomorphism between two groups

Published on 26 Mar 2026 - 6:27

441

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Classification of surjective group homomorphisms

Published on 11 Oct 2019 - 13:10

102

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Finding the possible kernels of homomorphisms $\mathbb{Z} \to \mathbb{Z}$.

Published on 13 Oct 2019 - 0:57

211

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Understanding the "triangle" argument to find a homomorphism from a direct product to a group and other instances of the argument

Published on 26 Mar 2026 - 11:01

104

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Is this homomorphism one-to-one?

Published on 14 Oct 2019 - 6:15

470

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Prove that $S_3$ and a subgroup $H$ of $S_4$ are isomorphic.

Published on 14 Oct 2019 - 10:46

77

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Why is this function not a group isomorphism?

Published on 17 Oct 2019 - 18:03

267

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Prove that $\varphi ^{−1}(K)$ is a subgroup of $G$

Published on 18 Oct 2019 - 0:15

269

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Homomorphisms of a Vector Space forms a Basis

Published on 20 Oct 2019 - 10:15

List Question

What is a continuous endomorphism of a group?

Proving isomorphism on additive group $(\Bbb{Z}_4,+)$ and multiplicative group $(\Bbb{Z}_5^*, \times)$

Is mapping generators to generators, and then extending, a well-defined homomorphism?

$H \subseteq G$. About the embedding(s?) of $\operatorname{Sym}(H)$ into $\operatorname{Sym}(G)$

Name of this homomorphism like mapping

How to simplify the Kernel of a homomorphism

At most one homomorphism between two groups

Classification of surjective group homomorphisms

Finding the possible kernels of homomorphisms $\mathbb{Z} \to \mathbb{Z}$.

Understanding the "triangle" argument to find a homomorphism from a direct product to a group and other instances of the argument

Is this homomorphism one-to-one?

Prove that $S_3$ and a subgroup $H$ of $S_4$ are isomorphic.

Why is this function not a group isomorphism?

Prove that $\varphi ^{−1}(K)$ is a subgroup of $G$

Homomorphisms of a Vector Space forms a Basis

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