List questions from group-homomorphism

Published on 04 Jan 2021 - 9:47

79

Views

For a commutative exact sequence show that $V_1$ and $V_3$ are finite dimensional iff $V_2$ and $V_4$ also are.

Published on 31 Mar 2026 - 17:54

199

Views

Fundamental Theorem of Homomorphism

Published on 07 Jan 2021 - 0:47

509

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Prove that if $\varphi$ is injective then $G \cong \varphi(G)$

Published on 14 Jan 2021 - 18:40

45

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Preimage of $A_{2k+1}$ in right multiplication action

Published on 14 Jan 2021 - 21:13

214

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Conjugation action on a semi-direct product $N\rtimes H$

Published on 15 Jan 2021 - 10:27

81

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statement of strong cayley's theorem

Published on 15 Jan 2021 - 14:54

357

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Does there exists any non-trivial group homomorphism from $\mathbb{R}$ to $\mathbb{Q}$

Published on 15 Jan 2021 - 15:43

113

Views

Relation between a group homomorphism and the composition with itself

Published on 16 Jan 2021 - 16:50

180

Views

surjective group homomorphism between $\mathbb{Z}^2$ and $\mathbb{Z}_{30}$

Published on 17 Jan 2021 - 0:42

81

Views

Prove that $\text{Aut}(\mathbb{Z}_{p^{n}} )\cong \mathbb{Z}_{\phi(p^{n})}$ where p is a prime and $\phi(.)$ denotes the euler totient function.

Published on 31 Mar 2026 - 18:37

63

Views

Homomorphisms of R-modules

Published on 18 Jan 2021 - 13:24

550

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The group of additive sequences of integers

Published on 19 Jan 2021 - 13:10

116

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Category Diagram of a Quotient Group

Published on 28 Mar 2026 - 10:33

58

Views

Alternative proof of Cayley's theorem works only for abelian groups

Published on 22 Jan 2021 - 13:37

List Question

Finding the kernel of homomorphism between two cyclic groups

For a commutative exact sequence show that $V_1$ and $V_3$ are finite dimensional iff $V_2$ and $V_4$ also are.

Fundamental Theorem of Homomorphism

Prove that if $\varphi$ is injective then $G \cong \varphi(G)$

Preimage of $A_{2k+1}$ in right multiplication action

Conjugation action on a semi-direct product $N\rtimes H$

statement of strong cayley's theorem

Does there exists any non-trivial group homomorphism from $\mathbb{R}$ to $\mathbb{Q}$

Relation between a group homomorphism and the composition with itself

surjective group homomorphism between $\mathbb{Z}^2$ and $\mathbb{Z}_{30}$

Prove that $\text{Aut}(\mathbb{Z}_{p^{n}} )\cong \mathbb{Z}_{\phi(p^{n})}$ where p is a prime and $\phi(.)$ denotes the euler totient function.

Homomorphisms of R-modules

The group of additive sequences of integers

Category Diagram of a Quotient Group

Alternative proof of Cayley's theorem works only for abelian groups

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