Question

If $f$ is a homomorphism, does it map $p$-groups to $p$-groups?

score 500 · Answer 1 · 2026-03-25 12:48:50

500

Views

If $f$ is a homomorphism, does it map $p$-groups to $p$-groups?

Published on 25 Mar 2026 - 12:48

score 151 · Answer 2 · 2019-09-28 19:24:14

151

Views

Homomorphism from $Q_8$ to $GL_2(\mathbb{C})$

Published on 28 Sep 2019 - 19:24

score 1k · Answer 3 · 2026-03-25 22:04:36

1k

Views

If a Subgroup has Finite Index in $\mathbb{Q} / \mathbb{Z}$ , Does it have Finite Index in $\mathbb{Q}$?

Published on 25 Mar 2026 - 22:04

score 57 · Answer 4 · 2019-09-29 17:14:54

57

Views

An epimorphism of $G=H \oplus \Bbb Z^N$ onto $G$, where $H$ is a finite abelian group

Published on 29 Sep 2019 - 17:14

score 166 · Answer 5 · 2019-10-01 11:04:51

166

Views

The anatomy of a homomorphism.

Published on 01 Oct 2019 - 11:04

score 257 · Answer 6 · 2019-10-01 14:36:02

257

Views

Example of finitely generated subgroup from Hungerford's algebra?

Published on 01 Oct 2019 - 14:36

score 13.6k · Answer 7 · 2014-07-20 21:15:50

13.6k

Views

Prove: A group $G$ is abelian if and only if the map $G\rightarrow G$ given by $x\mapsto x^{-1}$ is an automorphism.

Published on 20 Jul 2014 - 21:15

score 334 · Answer 8 · 2026-03-26 04:53:37

334

Views

How does $f_1(h)f_2(h)^{-1}$ generate a normal subgroup of $G_1 * G_2$?

Published on 26 Mar 2026 - 4:53

score 294 · Answer 9 · 2014-10-08 21:37:44

294

Views

Find all kinds of homomorphisms from $(\Bbb Z_n, +)$ to $(\Bbb C^*, \times)$.

Published on 08 Oct 2014 - 21:37

score 2.1k · Answer 10 · 2014-10-19 20:19:15

2.1k

Views

Image of Homomorphisms for Cyclic Groups

Published on 19 Oct 2014 - 20:19

score 44 · Answer 11 · 2014-10-28 01:39:12

44

Views

Does this group theory question require an additional hypothesis?

Published on 28 Oct 2014 - 1:39

score 435 · Answer 12 · 2014-11-07 20:19:33

435

Views

Consider $f: \mathbb Z_8 \rightarrow \mathbb Z_4$. List the cosets of the kernel of $f$

Published on 07 Nov 2014 - 20:19

score 6.7k · Answer 13 · 2014-12-03 10:22:23

6.7k

Views

Difference between homomorphisms and homomorphic images

Published on 03 Dec 2014 - 10:22

score 94 · Answer 14 · 2026-03-25 17:21:29

94

Views

Lie algebra of a semi-direct product of Lie groups

Published on 25 Mar 2026 - 17:21

score 281 · Answer 15 · 2019-10-02 22:41:44

281

Views

Examples of non-abelian groups $G$ such that $\operatorname{Hom}(G,H)$ is abelian.

Published on 02 Oct 2019 - 22:41

List Question

If $f$ is a homomorphism, does it map $p$-groups to $p$-groups?

Homomorphism from $Q_8$ to $GL_2(\mathbb{C})$

If a Subgroup has Finite Index in $\mathbb{Q} / \mathbb{Z}$ , Does it have Finite Index in $\mathbb{Q}$?

An epimorphism of $G=H \oplus \Bbb Z^N$ onto $G$, where $H$ is a finite abelian group

The anatomy of a homomorphism.

Example of finitely generated subgroup from Hungerford's algebra?

Prove: A group $G$ is abelian if and only if the map $G\rightarrow G$ given by $x\mapsto x^{-1}$ is an automorphism.

How does $f_1(h)f_2(h)^{-1}$ generate a normal subgroup of $G_1 * G_2$?

Find all kinds of homomorphisms from $(\Bbb Z_n, +)$ to $(\Bbb C^*, \times)$.

Image of Homomorphisms for Cyclic Groups

Does this group theory question require an additional hypothesis?

Consider $f: \mathbb Z_8 \rightarrow \mathbb Z_4$. List the cosets of the kernel of $f$

Difference between homomorphisms and homomorphic images

Lie algebra of a semi-direct product of Lie groups

Examples of non-abelian groups $G$ such that $\operatorname{Hom}(G,H)$ is abelian.

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