List questions from group-homomorphism

Published on 22 Mar 2021 - 19:38

146

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Homomorphisms of abelian group homomorphisms

Published on 25 Mar 2021 - 2:43

205

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Proof that the intersection of all conjugates of a subgroup is normal.

Published on 25 Mar 2021 - 11:57

482

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Taking $G$-invariants over a short exact sequence of $G$-modules

Published on 31 Mar 2026 - 22:50

86

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Construction of a surjective group homomorphism

Published on 04 Apr 2021 - 5:59

36

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Normal subgroups and Homomorphism

Published on 04 Apr 2021 - 10:21

62

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Image of a self-normalizing subgroup under a surjective homomorphism

Published on 05 Apr 2021 - 15:02

50

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Lemma of Characterictic Subgroups

Published on 23 Feb 2026 - 7:19

68

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Question Regarding Atiyah&Macdonald Chapter 2 Ex.10

Published on 07 Apr 2021 - 15:36

713

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Let $\varphi:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic, and if $G$ is abelian, then $G'$ is abelian.

Published on 07 Apr 2021 - 20:12

251

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Artin exercise 2.5.4: Let $f:\Bbb R^+\to\Bbb C^\times$ be the map $f(x)=e^{ix}$. Prove that $f$ is a homomorphism, and determine its kernel and image.

Published on 09 Apr 2021 - 19:29

193

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Homomorphism from trivial group to $\mathbb{Z}_{5n}$

Published on 11 Apr 2021 - 10:43

533

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Proving that the quotient map is a surjective group homomorphism

Published on 28 Mar 2026 - 15:46

171

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How do I find all homomorphisms between $S_3 \to \mathbb{Z}_{15}$?

Published on 29 Mar 2026 - 13:41

99

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Show that the group of all complex $2^n$th roots of unity, $n=0,1,2,...$, has a fully-invariant subgroup which is not verbal

Published on 23 Feb 2026 - 5:47

List Question

Order of an element given a homomorphism

Homomorphisms of abelian group homomorphisms

Proof that the intersection of all conjugates of a subgroup is normal.

Taking $G$-invariants over a short exact sequence of $G$-modules

Construction of a surjective group homomorphism

Normal subgroups and Homomorphism

Image of a self-normalizing subgroup under a surjective homomorphism

Lemma of Characterictic Subgroups

Question Regarding Atiyah&Macdonald Chapter 2 Ex.10

Let $\varphi:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic, and if $G$ is abelian, then $G'$ is abelian.

Artin exercise 2.5.4: Let $f:\Bbb R^+\to\Bbb C^\times$ be the map $f(x)=e^{ix}$. Prove that $f$ is a homomorphism, and determine its kernel and image.

Homomorphism from trivial group to $\mathbb{Z}_{5n}$

Proving that the quotient map is a surjective group homomorphism

How do I find all homomorphisms between $S_3 \to \mathbb{Z}_{15}$?

Show that the group of all complex $2^n$th roots of unity, $n=0,1,2,...$, has a fully-invariant subgroup which is not verbal

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