List questions from group-homomorphism

Published on 14 Dec 2021 - 4:40

109

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Showing that for $G = \langle x \rangle$ if $|G|$ is odd, then $\phi$ is an injection.

Published on 15 Dec 2021 - 19:35

51

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Consequence of the first isomorphism theorem

Published on 16 Dec 2021 - 18:08

42

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Showing the existence of an automorphism between two semidirect products

Published on 26 Mar 2026 - 12:36

50

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Prove $j:D\to \text{Hom}_R(S,S)$ is left $S$-module homomorphism

Published on 21 Dec 2021 - 16:13

103

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Graded algebras and symbols

Published on 25 Mar 2026 - 16:01

43

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How do I prove that the image of a cyclic group has the following property?

Published on 25 Dec 2021 - 8:55

121

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Kernel of homomorphism $\phi:A\to Z(A)$ where $A$ is a group

Published on 25 Dec 2021 - 17:31

240

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Homomorphism and preservation of structure

Published on 29 Dec 2021 - 15:24

65

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Is there an injective homomorphism between $\mathbb{Z}_{20}^{}$ and $\mathbb{Z}_{64}^{}$

Published on 31 Dec 2021 - 14:41

244

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Is there an injective homomorphism between $\mathbb{Z_4} \times \mathbb{Z_4}$ and $S_7$?

Published on 31 Dec 2021 - 19:30

139

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Proving that the kernel of a homomorphism is exactly equal to a normal subgroup $A'$

Published on 31 Dec 2021 - 22:58

43

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What is this property of the actions useful for?

Published on 05 Jan 2022 - 9:09

83

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For $P$ the set of all primes, ${\rm Hom}(\Bbb Z,\sum_{p\in P}\Bbb Z_p)\not\cong\prod_{p\in P}{\rm Hom}(\Bbb Z,\Bbb Z_p)$

Published on 28 Mar 2026 - 20:14

185

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Centers and Onto Group Homomorphism

Published on 06 Jan 2022 - 19:28

List Question

Is it necessary to determine a definite homomorphism here?

Showing that for $G = \langle x \rangle$ if $|G|$ is odd, then $\phi$ is an injection.

Consequence of the first isomorphism theorem

Showing the existence of an automorphism between two semidirect products

Prove $j:D\to \text{Hom}_R(S,S)$ is left $S$-module homomorphism

Graded algebras and symbols

How do I prove that the image of a cyclic group has the following property?

Kernel of homomorphism $\phi:A\to Z(A)$ where $A$ is a group

Homomorphism and preservation of structure

Is there an injective homomorphism between $\mathbb{Z}_{20}^{}$ and $\mathbb{Z}_{64}^{}$

Is there an injective homomorphism between $\mathbb{Z_4} \times \mathbb{Z_4}$ and $S_7$?

Proving that the kernel of a homomorphism is exactly equal to a normal subgroup $A'$

What is this property of the actions useful for?

For $P$ the set of all primes, ${\rm Hom}(\Bbb Z,\sum_{p\in P}\Bbb Z_p)\not\cong\prod_{p\in P}{\rm Hom}(\Bbb Z,\Bbb Z_p)$

Centers and Onto Group Homomorphism

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