Question

Do there exist a nontrivial group homomorphism from $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{Z},+)?$

score 102 · Answer 1 · 2021-07-26 15:39:54

102

Views

Do there exist a nontrivial group homomorphism from $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{Z},+)?$

Published on 26 Jul 2021 - 15:39

score 364 · Answer 2 · 2021-07-30 21:05:22

364

Views

Homomorphisms from $\mathbb{Z}_{20}$ to $\mathbb{Z}_8$

Published on 30 Jul 2021 - 21:05

score 83 · Answer 3 · 2026-03-28 22:53:29

83

Views

Does a group morphism factor through a quotient group?

Published on 28 Mar 2026 - 22:53

score 50 · Answer 4 · 2021-08-01 18:45:03

50

Views

Take $G$ a group such that ${\rm Hom}(G,\mathbb{R})=0$. Prove that $G$ is a finite group

Published on 01 Aug 2021 - 18:45

score 190 · Answer 5 · 2021-08-02 16:16:35

190

Views

Let $\mu:A\to B$ be mono of abelian groups and let $G$ be torsion-free abelian. Prove $\mu_*:A⊗_\Bbb ZG\to B⊗_\Bbb ZG$ is mono

Published on 02 Aug 2021 - 16:16

score 82 · Answer 6 · 2021-08-04 20:15:24

82

Views

Why does $\rho(n) = \rho(1 + \dots + 1) = \rho(1)^n$. where $\rho$ is a homomorphism?

Published on 04 Aug 2021 - 20:15

score 283 · Answer 7 · 2021-08-07 04:55:01

283

Views

Group of homomorphisms from $\mathbb{R}/\mathbb{Z}$ to itself

Published on 07 Aug 2021 - 4:55

score 49 · Answer 8 · 2021-08-15 20:48:35

49

Views

Why is the one-parameter group constant?

Published on 15 Aug 2021 - 20:48

score 80 · Answer 9 · 2026-03-30 16:46:19

80

Views

Semidirect products via $\rho\colon B\to \mathrm{Aut}(A)$

Published on 30 Mar 2026 - 16:46

score 245 · Answer 10 · 2026-03-30 16:41:45

245

Views

Classifying abelian numbers

Published on 30 Mar 2026 - 16:41

score 65 · Answer 11 · 2021-08-19 04:13:47

65

Views

extension of group homomorphism to ring homomorphism

Published on 19 Aug 2021 - 4:13

score 63 · Answer 12 · 2021-08-20 10:56:23

63

Views

Let $G = ( \Bbb Z \times \Bbb Z , +)$ and $H = ( \Bbb Z, +).$ Also define $A = \{(x,x) \mid x \in \Bbb Z \}$. Show that $G / A \cong H$

Published on 20 Aug 2021 - 10:56

score 193 · Answer 13 · 2026-02-23 19:23:37

193

Views

Surjective homomorphism into a magma confers all the algebraic properties of the domain

Published on 23 Feb 2026 - 19:23

score 274 · Answer 14 · 2021-08-26 05:20:19

274

Views

How many group homomorphisms from $\mathbb{Q/Z\to Q}$ are there?

Published on 26 Aug 2021 - 5:20

score 213 · Answer 15 · 2021-08-27 21:49:48

213

Views

Let $G$ be a group, $g\in G$. Let $\varphi_g:G\to G$ s.t. $\varphi_g(x)=gx$ for $x\in G$. For which $g\in G$ is $\varphi_g$ a homomorphism?

Published on 27 Aug 2021 - 21:49

List Question

Do there exist a nontrivial group homomorphism from $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{Z},+)?$

Homomorphisms from $\mathbb{Z}_{20}$ to $\mathbb{Z}_8$

Does a group morphism factor through a quotient group?

Take $G$ a group such that ${\rm Hom}(G,\mathbb{R})=0$. Prove that $G$ is a finite group

Let $\mu:A\to B$ be mono of abelian groups and let $G$ be torsion-free abelian. Prove $\mu_*:A⊗_\Bbb ZG\to B⊗_\Bbb ZG$ is mono

Why does $\rho(n) = \rho(1 + \dots + 1) = \rho(1)^n$. where $\rho$ is a homomorphism?

Group of homomorphisms from $\mathbb{R}/\mathbb{Z}$ to itself

Why is the one-parameter group constant?

Semidirect products via $\rho\colon B\to \mathrm{Aut}(A)$

Classifying abelian numbers

extension of group homomorphism to ring homomorphism

Let $G = ( \Bbb Z \times \Bbb Z , +)$ and $H = ( \Bbb Z, +).$ Also define $A = \{(x,x) \mid x \in \Bbb Z \}$. Show that $G / A \cong H$

Surjective homomorphism into a magma confers all the algebraic properties of the domain

How many group homomorphisms from $\mathbb{Q/Z\to Q}$ are there?

Let $G$ be a group, $g\in G$. Let $\varphi_g:G\to G$ s.t. $\varphi_g(x)=gx$ for $x\in G$. For which $g\in G$ is $\varphi_g$ a homomorphism?

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