Question

Homomorphism from $\mathbb{Z}_p \to \mathrm{Aut}(\mathbb{Z}_p)$ for $p$ prime

score 99 · Answer 1 · 2023-11-09 07:27:43

99

Views

Homomorphism from $\mathbb{Z}_p \to \mathrm{Aut}(\mathbb{Z}_p)$ for $p$ prime

Published on 09 Nov 2023 - 7:27

score 91 · Answer 2 · 2023-11-10 06:11:39

91

Views

Does there exists a nontrivial group homomorphism from $\Bbb{Q}/\Bbb{Z}$ to $\Bbb{Z}/2^n\Bbb{Z}$ ($n\in \Bbb{Z}$)?

Published on 10 Nov 2023 - 6:11

score 50 · Answer 3 · 2023-11-10 07:38:05

50

Views

Let $V$ and $W$ be vector spaces over $K$ and $f: V \to W$ a Homomorphism. Prove that this is a Homomorphism: $f^: V^ \to W^*, g \to g \circ f$

Published on 10 Nov 2023 - 7:38

score 76 · Answer 4 · 2023-11-12 16:13:00

76

Views

Let $A,B, C,A',B'$ be an abelian groups. Let $f:A\to B$ and $g:B\to C$ be group homomorphisms.

Published on 12 Nov 2023 - 16:13

score 103 · Answer 5 · 2023-11-18 12:38:37

103

Views

Is order of Image of $A\times B$ under group homomorphism is smaller than that of $B$ when there is no nontrivial homomorphism from $A$ to target?

Published on 18 Nov 2023 - 12:38

score 64 · Answer 6 · 2023-11-22 17:24:55

64

Views

Find Kernel of a group homomorphism

Published on 22 Nov 2023 - 17:24

score 204 · Answer 7 · 2023-11-25 20:36:05

204

Views

The unit circle of a field has an injective homomorphism to the group of units.

Published on 25 Nov 2023 - 20:36

score 100 · Answer 8 · 2023-11-27 10:41:33

100

Views

Isomorphism between quotient of p adic units and quotient of $\mathbb{F}_{p}^{\times }$

Published on 27 Nov 2023 - 10:41

score 130 · Answer 9 · 2023-11-29 12:02:57

130

Views

If we know any homomorphism between fixed group $G$ and arbitrary group $F$, could we determine $G$?

Published on 29 Nov 2023 - 12:02

score 209 · Answer 10 · 2023-12-03 18:23:55

209

Views

If G is a finite abelian group, prove that $o(G) = o(\hat{G})$ and G is isomorphic to $\hat{G}$.

Published on 03 Dec 2023 - 18:23

score 46 · Answer 11 · 2023-12-03 20:00:56

46

Views

Show that there is a homomorphism with $\operatorname{kernel}(f) \subseteq H$

Published on 03 Dec 2023 - 20:00

score 56 · Answer 12 · 2026-03-29 16:47:53

56

Views

GNS representations with $\hat{G}$ and $C^*$-algebras

Published on 29 Mar 2026 - 16:47

score 70 · Answer 13 · 2026-02-23 18:43:25

70

Views

Show that $\lambda:G \to \mathbb{R}^\ast$ where $R_h^\ast \mu = \lambda (h) \mu$ is smooth

Published on 23 Feb 2026 - 18:43

score 99 · Answer 14 · 2026-03-25 10:56:56

99

Views

Comparing order of $\ker f$ and $\ker\tilde{f}$

Published on 25 Mar 2026 - 10:56

score 203 · Answer 15 · 2026-03-27 04:24:15

203

Views

First Isomorphism Theorem not concerned with Injectivity?

Published on 27 Mar 2026 - 4:24

List Question

Homomorphism from $\mathbb{Z}_p \to \mathrm{Aut}(\mathbb{Z}_p)$ for $p$ prime

Does there exists a nontrivial group homomorphism from $\Bbb{Q}/\Bbb{Z}$ to $\Bbb{Z}/2^n\Bbb{Z}$ ($n\in \Bbb{Z}$)?

Let $V$ and $W$ be vector spaces over $K$ and $f: V \to W$ a Homomorphism. Prove that this is a Homomorphism: $f^: V^ \to W^*, g \to g \circ f$

Let $A,B, C,A',B'$ be an abelian groups. Let $f:A\to B$ and $g:B\to C$ be group homomorphisms.

Is order of Image of $A\times B$ under group homomorphism is smaller than that of $B$ when there is no nontrivial homomorphism from $A$ to target?

Find Kernel of a group homomorphism

The unit circle of a field has an injective homomorphism to the group of units.

Isomorphism between quotient of p adic units and quotient of $\mathbb{F}_{p}^{\times }$

If we know any homomorphism between fixed group $G$ and arbitrary group $F$, could we determine $G$?

If G is a finite abelian group, prove that $o(G) = o(\hat{G})$ and G is isomorphic to $\hat{G}$.

Show that there is a homomorphism with $\operatorname{kernel}(f) \subseteq H$

GNS representations with $\hat{G}$ and $C^*$-algebras

Show that $\lambda:G \to \mathbb{R}^\ast$ where $R_h^\ast \mu = \lambda (h) \mu$ is smooth

Comparing order of $\ker f$ and $\ker\tilde{f}$

First Isomorphism Theorem not concerned with Injectivity?

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