Question

Prove that if H is a group of odd order, there exists no nontrivial homomorphism from D_2017 to H?

score 516 · Answer 1 · 2026-04-15 10:20:56

516

Views

Prove that if H is a group of odd order, there exists no nontrivial homomorphism from D_2017 to H?

Published on 15 Apr 2026 - 10:20

score 1.1k · Answer 2 · 2026-04-17 07:20:28

1.1k

Views

If $\varphi: R^m \to R^n$ is an surjective module homomorphism, show $n \leq m$.

Published on 17 Apr 2026 - 7:20

score 388 · Answer 3 · 2026-05-10 12:34:39

388

Views

Prove that there do not exist non-trivial groups $H$ and $K$ such that $\mathbb{Q}\cong H\times K$.

Published on 10 May 2026 - 12:34

score 416 · Answer 4 · 2026-04-12 21:24:16

416

Views

Prove that $\sum_{a\in A} φ(a)=0$ where $A$ is finite Abelian group.

Published on 12 Apr 2026 - 21:24

score 2.3k · Answer 5 · 2026-04-13 10:44:00

2.3k

Views

Is there Any Homomorphism Between Vector Spaces that is not Linear?

Published on 13 Apr 2026 - 10:44

score 122 · Answer 6 · 2026-05-10 16:57:16

122

Views

A permutation of $\mathbb{Z}/n\mathbb{Z}$ disturbing distances is a group homomorphism?

Published on 10 May 2026 - 16:57

score 496 · Answer 7 · 2026-04-16 21:21:30

496

Views

Surjective homomorphisms from Free group of rank 2 to Finite group of order 2/

Published on 16 Apr 2026 - 21:21

score 37 · Answer 8 · 2026-04-11 20:00:14

37

Views

Understanding all homomorphisms $\alpha: \mathbb{Z}^a \to \mathbb{Z}^b$ and their matrix representations

Published on 11 Apr 2026 - 20:00

score 51 · Answer 9 · 2026-04-13 16:59:43

51

Views

Prove that the function $f(\bar{z})=e^{2\pi i z}$ is well-defined and that it is a group-homomorphism

Published on 13 Apr 2026 - 16:59

score 52 · Answer 10 · 2026-04-29 12:50:59

52

Views

Relation between homomorphisms and monomorphims of finite groups

Published on 29 Apr 2026 - 12:50

score 165 · Answer 11 · 2026-04-11 14:10:28

165

Views

Understanding Advanced Permutation Group by Example

Published on 11 Apr 2026 - 14:10

score 115 · Answer 12 · 2026-04-14 06:43:17

115

Views

What a group homomorphism looks like

Published on 14 Apr 2026 - 6:43

score 632 · Answer 13 · 2026-05-05 03:24:51

632

Views

$f (e_G )=e_H $ is necessary for Monoid homomorphisms

Published on 05 May 2026 - 3:24

score 650 · Answer 14 · 2026-04-12 11:47:55

650

Views

Proving a group homomorphism of a cartesian product, what are the operations?

Published on 12 Apr 2026 - 11:47

score 653 · Answer 15 · 2026-04-15 23:50:27

653

Views

Restriction of homomorphism to finite index subgroup gives finite index subgroup of kernel

Published on 15 Apr 2026 - 23:50

List Question

Prove that if H is a group of odd order, there exists no nontrivial homomorphism from D_2017 to H?

If $\varphi: R^m \to R^n$ is an surjective module homomorphism, show $n \leq m$.

Prove that there do not exist non-trivial groups $H$ and $K$ such that $\mathbb{Q}\cong H\times K$.

Prove that $\sum_{a\in A} φ(a)=0$ where $A$ is finite Abelian group.

Is there Any Homomorphism Between Vector Spaces that is not Linear?

A permutation of $\mathbb{Z}/n\mathbb{Z}$ disturbing distances is a group homomorphism?

Surjective homomorphisms from Free group of rank 2 to Finite group of order 2/

Understanding all homomorphisms $\alpha: \mathbb{Z}^a \to \mathbb{Z}^b$ and their matrix representations

Prove that the function $f(\bar{z})=e^{2\pi i z}$ is well-defined and that it is a group-homomorphism

Relation between homomorphisms and monomorphims of finite groups

Understanding Advanced Permutation Group by Example

What a group homomorphism looks like

$f (e_G )=e_H $ is necessary for Monoid homomorphisms

Proving a group homomorphism of a cartesian product, what are the operations?

Restriction of homomorphism to finite index subgroup gives finite index subgroup of kernel

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