Question

A finite normal subgroup is a subset of the center

score 547 · Answer 1 · 2026-05-10 17:38:43

547

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A finite normal subgroup is a subset of the center

Published on 10 May 2026 - 17:38

score 52 · Answer 2 · 2026-04-17 01:56:05

52

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If $\lvert\ker(\varphi)\rvert=p$ and $p$ is prime, then $G=\ker(\varphi)$

Published on 17 Apr 2026 - 1:56

score 1.9k · Answer 3 · 2026-05-06 03:39:45

1.9k

Views

A group homomorphism from $GL(n,\Bbb {R})$ such that $SL(n,\Bbb {R})$ is the kernel

Published on 06 May 2026 - 3:39

score 132 · Answer 4 · 2026-04-15 21:57:30

132

Views

Proof: There can be no non-zero homomorphism from $(\Bbb Z_4,+)$ to $(\Bbb Z_5,+)$

Published on 15 Apr 2026 - 21:57

score 267 · Answer 5 · 2026-04-14 18:03:30

267

Views

If $f$ is a homomorphism then it is one-to-one or onto

Published on 14 Apr 2026 - 18:03

score 739 · Answer 6 · 2026-04-15 18:09:26

739

Views

For every integer $n \geq 2$ , there is a unique non-trivial homomorphism $f: {S_n} \to \mathbb{C^*}$.

Published on 15 Apr 2026 - 18:09

score 348 · Answer 7 · 2026-05-10 14:32:07

348

Views

Homomorphism between free groups induced by group homomorphism of abelian groups.

Published on 10 May 2026 - 14:32

score 160 · Answer 8 · 2026-05-10 19:14:37

160

Views

Nontrivial homomorphism from a connected topological group to a discrete group?

Published on 10 May 2026 - 19:14

score 2.8k · Answer 9 · 2026-04-15 17:33:27

2.8k

Views

Describe all group homomorphisms from Z×Z into Z

Published on 15 Apr 2026 - 17:33

score 153 · Answer 10 · 2026-05-10 14:32:08

153

Views

image of homomorphism contains free group, then so does domain

Published on 10 May 2026 - 14:32

score 463 · Answer 11 · 2026-04-10 17:26:43

463

Views

Counting Homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$

Published on 10 Apr 2026 - 17:26

score 355 · Answer 12 · 2026-04-17 02:59:21

355

Views

Slight generalization of the First Isomorphism Theorem

Published on 17 Apr 2026 - 2:59

score 538 · Answer 13 · 2026-04-14 05:56:13

538

Views

Determine the number of surjective Homomorphism.

Published on 14 Apr 2026 - 5:56

score 125 · Answer 14 · 2026-04-08 17:42:18

125

Views

Surjective Homomorphism $f : \mathbb{Z}/12\mathbb{Z}\times \mathbb{Z}/6\mathbb{Z}\longrightarrow\mathbb{Z}/6\mathbb{Z}$.

Published on 08 Apr 2026 - 17:42

score 350 · Answer 15 · 2026-04-15 02:15:02

350

Views

Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$

Published on 15 Apr 2026 - 2:15

List Question

A finite normal subgroup is a subset of the center

If $\lvert\ker(\varphi)\rvert=p$ and $p$ is prime, then $G=\ker(\varphi)$

A group homomorphism from $GL(n,\Bbb {R})$ such that $SL(n,\Bbb {R})$ is the kernel

Proof: There can be no non-zero homomorphism from $(\Bbb Z_4,+)$ to $(\Bbb Z_5,+)$

If $f$ is a homomorphism then it is one-to-one or onto

For every integer $n \geq 2$ , there is a unique non-trivial homomorphism $f: {S_n} \to \mathbb{C^*}$.

Homomorphism between free groups induced by group homomorphism of abelian groups.

Nontrivial homomorphism from a connected topological group to a discrete group?

Describe all group homomorphisms from Z×Z into Z

image of homomorphism contains free group, then so does domain

Counting Homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$

Slight generalization of the First Isomorphism Theorem

Determine the number of surjective Homomorphism.

Surjective Homomorphism $f : \mathbb{Z}/12\mathbb{Z}\times \mathbb{Z}/6\mathbb{Z}\longrightarrow\mathbb{Z}/6\mathbb{Z}$.

Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$

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