List questions from group-homomorphism

Published on 20 Sep 2022 - 0:04

225

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Complexification of $O(n,\mathbb{R})$

Published on 28 Mar 2026 - 6:14

62

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Homomorphism from $Q_8$ to cyclic group of order $2$

Published on 25 Sep 2022 - 21:25

882

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Question about the definition of a homomorphism

Published on 30 Mar 2026 - 23:18

113

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Inverse bijections between subgroups of $G$ containing the kernel and subgroups of $H$ contained in the image.

Published on 05 Oct 2022 - 20:49

77

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Generators and Relations and Homomorphisms

Published on 30 Mar 2026 - 6:48

148

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Are $\Bbb{R}$ and $\Bbb{Z}\times\Bbb{R}$ isomorphic as groups?

Published on 09 Oct 2022 - 5:01

64

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Order of $\langle f(g)\rangle$

Published on 11 Oct 2022 - 3:11

95

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What are the group-homomorphisms $f: S_n\rightarrow \mathbb{C}^*$?

Published on 13 Oct 2022 - 15:45

249

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Kernel is the normal closure

Published on 13 Oct 2022 - 18:21

210

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Connecting map in the long exact sequence of homotopy groups

Published on 29 Mar 2026 - 11:44

134

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Show that no group homomorphism $h : \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$ is injective.

Published on 16 Oct 2022 - 21:14

68

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Why is $f(n) = g^n$ a homomorphism?

Published on 19 Oct 2022 - 19:08

46

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A question related to an induced homomorphism between two groups

Published on 23 Feb 2026 - 20:40

67

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Kernels of homomorphisms of an algebra are only its two-sided ideals

Published on 21 Oct 2022 - 14:56

List Question

If $\phi(\phi(g))=g$ then show that $G\cong \phi(G) \times \text{ker }\phi$

Complexification of $O(n,\mathbb{R})$

Homomorphism from $Q_8$ to cyclic group of order $2$

Question about the definition of a homomorphism

Inverse bijections between subgroups of $G$ containing the kernel and subgroups of $H$ contained in the image.

Generators and Relations and Homomorphisms

Are $\Bbb{R}$ and $\Bbb{Z}\times\Bbb{R}$ isomorphic as groups?

Order of $\langle f(g)\rangle$

What are the group-homomorphisms $f: S_n\rightarrow \mathbb{C}^*$?

Kernel is the normal closure

Connecting map in the long exact sequence of homotopy groups

Show that no group homomorphism $h : \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$ is injective.

Why is $f(n) = g^n$ a homomorphism?

A question related to an induced homomorphism between two groups

Kernels of homomorphisms of an algebra are only its two-sided ideals

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