Question

Prove that $G\cong H\times K$ if and only if there are homomorphisms...

score 322 · Answer 1 · 2026-03-28 21:51:40

322

Views

Prove that $G\cong H\times K$ if and only if there are homomorphisms...

Published on 28 Mar 2026 - 21:51

score 42 · Answer 2 · 2022-05-12 13:22:35

42

Views

Prove that $D$ is a field.

Published on 12 May 2022 - 13:22

score 73 · Answer 3 · 2022-05-17 13:59:46

73

Views

Prove that there is no homomorphism from $S_5$ onto a group of order $24$.

Published on 17 May 2022 - 13:59

score 30 · Answer 4 · 2022-05-17 19:37:46

30

Views

A surjective morphism of groups takes finitely generated subgroups into finitely generated subgroups

Published on 17 May 2022 - 19:37

score 96 · Answer 5 · 2022-05-17 23:56:20

96

Views

Homomorphism between $\mathbb{Z}/m$ and $\mathbb{Z}/n$

Published on 17 May 2022 - 23:56

score 487 · Answer 6 · 2022-05-19 21:44:02

487

Views

Does there exist a surjective group homomorphism $\varphi:A_4\rightarrow\mathbb{Z}/4\mathbb{Z}$?

Published on 19 May 2022 - 21:44

score 252 · Answer 7 · 2022-05-23 17:39:52

252

Views

Homomorphism and Isomorphism importance

Published on 23 May 2022 - 17:39

score 582 · Answer 8 · 2022-05-24 13:50:18

582

Views

Is $\text{GL}_2(\mathbb{R})/\mathbb{R}^{\times}$ isomorphic to $\text{SL}_2(\mathbb{R})$?

Published on 24 May 2022 - 13:50

score 96 · Answer 9 · 2022-05-24 17:00:34

96

Views

A link between multiplicative function on endomorphisms and their determinants

Published on 24 May 2022 - 17:00

score 66 · Answer 10 · 2026-04-05 11:59:26

66

Views

Let $\phi : G\to G'$ be a homomorphism and let $S'\subseteq G'$. Is $\phi^{-1}(\langle S'\rangle ) = \langle \phi^{-1}(S')\rangle$?

Published on 05 Apr 2026 - 11:59

score 141 · Answer 11 · 2026-03-28 04:35:48

141

Views

Prove: there exist a unique group homomorphism $\bar{f}: G_1/H_1 \to G_2/H_2$

Published on 28 Mar 2026 - 4:35

score 36 · Answer 12 · 2026-03-28 04:34:49

36

Views

Why $\bar{f}(x + H_1) = f(x) + H_2$?

Published on 28 Mar 2026 - 4:34

score 215 · Answer 13 · 2022-06-01 22:03:06

215

Views

Prove that the conjugate of $h$ by $g$ is an isomorphism

Published on 01 Jun 2022 - 22:03

score 40 · Answer 14 · 2022-06-05 09:27:23

40

Views

Prove $\phi^{-1}(\phi(H))=\langle H,\ker\phi \rangle$

Published on 05 Jun 2022 - 9:27

score 62 · Answer 15 · 2026-03-30 13:59:14

62

Views

The set of irrational characters is dense in $\text{Hom}(G,\mathbb{R})$ for finitely generated $G$.

Published on 30 Mar 2026 - 13:59

List Question

Prove that $G\cong H\times K$ if and only if there are homomorphisms...

Prove that $D$ is a field.

Prove that there is no homomorphism from $S_5$ onto a group of order $24$.

A surjective morphism of groups takes finitely generated subgroups into finitely generated subgroups

Homomorphism between $\mathbb{Z}/m$ and $\mathbb{Z}/n$

Does there exist a surjective group homomorphism $\varphi:A_4\rightarrow\mathbb{Z}/4\mathbb{Z}$?

Homomorphism and Isomorphism importance

Is $\text{GL}_2(\mathbb{R})/\mathbb{R}^{\times}$ isomorphic to $\text{SL}_2(\mathbb{R})$?

A link between multiplicative function on endomorphisms and their determinants

Let $\phi : G\to G'$ be a homomorphism and let $S'\subseteq G'$. Is $\phi^{-1}(\langle S'\rangle ) = \langle \phi^{-1}(S')\rangle$?

Prove: there exist a unique group homomorphism $\bar{f}: G_1/H_1 \to G_2/H_2$

Why $\bar{f}(x + H_1) = f(x) + H_2$?

Prove that the conjugate of $h$ by $g$ is an isomorphism

Prove $\phi^{-1}(\phi(H))=\langle H,\ker\phi \rangle$

The set of irrational characters is dense in $\text{Hom}(G,\mathbb{R})$ for finitely generated $G$.

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