Question

Does a functor from one category to another imply homomorphism between automorphism groups.

score 41 · Answer 1 · 2026-03-27 12:16:19

41

Views

Does a functor from one category to another imply homomorphism between automorphism groups.

Published on 27 Mar 2026 - 12:16

score 84 · Answer 2 · 2024-03-19 18:53:55

84

Views

Why must an automorphism of $Z_n$ be of the form $x \mapsto x^a$?

Published on 19 Mar 2024 - 18:53

score 142 · Answer 3 · 2024-03-20 15:43:38

142

Views

Without choice, what can be the (finite) automorphism groups of $\mathbb F_2$-vector spaces?

Published on 20 Mar 2024 - 15:43

score 40 · Answer 4 · 2024-03-28 14:15:03

40

Views

Is there any substantial study regarding the automorphism of the field $k((x_1,\cdots, x_n)):=\text{Frac}(k[[x_1, \cdots, x_n]])$?

Published on 28 Mar 2024 - 14:15

score 36 · Answer 5 · 2024-03-28 23:00:51

36

Views

Finite group $G$ with $\alpha \in \text{Aut}(G)$ such that $x^{\alpha} \neq x = x^{{\alpha}^2}$

Published on 28 Mar 2024 - 23:00

score 6.8k · Answer 6 · 2026-03-27 04:17:43

6.8k

Views

Automorphism group of direct product of groups

Published on 27 Mar 2026 - 4:17

score 501 · Answer 7 · 2015-04-25 18:21:43

501

Views

Wanted: Group homomorphism $\operatorname{Aut}(G) \to H$ whose kernel is the set of inner automorphisms

Published on 25 Apr 2015 - 18:21

score 126 · Answer 8 · 2015-04-27 15:43:37

126

Views

Finding Homomorphisms From a Cyclic Group to an Automorphism Group.

Published on 27 Apr 2015 - 15:43

score 483 · Answer 9 · 2026-02-23 05:40:42

483

Views

Characteristic subgroups of Aut(G)

Published on 23 Feb 2026 - 5:40

score 498 · Answer 10 · 2015-06-30 20:32:34

498

Views

$\operatorname{Aut}(G)\cong \Bbb{Z}/8\Bbb{Z}$

Published on 30 Jun 2015 - 20:32

score 269 · Answer 11 · 2015-10-09 20:28:41

269

Views

Proving $\mathrm{Aut}(S_{n}) = S_{n}$ for $n > 6$

Published on 09 Oct 2015 - 20:28

score 109 · Answer 12 · 2026-03-02 06:22:17

109

Views

Prove that the map from $H$ to $\operatorname{Aut}(K)$ which sends each $h \in H$ to an automorphism sending $k$ to $k^h$ is an homomorphism.

Published on 02 Mar 2026 - 6:22

score 6.5k · Answer 13 · 2026-03-23 03:51:58

6.5k

Views

${\rm Aut}(G)$ is cyclic $\implies G$ is abelian

Published on 23 Mar 2026 - 3:51

score 201 · Answer 14 · 2026-03-07 05:22:54

201

Views

Graph Automorphisms and Induced Subgraphs

Published on 07 Mar 2026 - 5:22

score 3.3k · Answer 15 · 2026-03-07 11:00:22

3.3k

Views

There does not exist group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_n$ (for odd $n$)

Published on 07 Mar 2026 - 11:00

List Question

Does a functor from one category to another imply homomorphism between automorphism groups.

Why must an automorphism of $Z_n$ be of the form $x \mapsto x^a$?

Without choice, what can be the (finite) automorphism groups of $\mathbb F_2$-vector spaces?

Is there any substantial study regarding the automorphism of the field $k((x_1,\cdots, x_n)):=\text{Frac}(k[[x_1, \cdots, x_n]])$?

Finite group $G$ with $\alpha \in \text{Aut}(G)$ such that $x^{\alpha} \neq x = x^{{\alpha}^2}$

Automorphism group of direct product of groups

Wanted: Group homomorphism $\operatorname{Aut}(G) \to H$ whose kernel is the set of inner automorphisms

Finding Homomorphisms From a Cyclic Group to an Automorphism Group.

Characteristic subgroups of Aut(G)

$\operatorname{Aut}(G)\cong \Bbb{Z}/8\Bbb{Z}$

Proving $\mathrm{Aut}(S_{n}) = S_{n}$ for $n > 6$

Prove that the map from $H$ to $\operatorname{Aut}(K)$ which sends each $h \in H$ to an automorphism sending $k$ to $k^h$ is an homomorphism.

${\rm Aut}(G)$ is cyclic $\implies G$ is abelian

Graph Automorphisms and Induced Subgraphs

There does not exist group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_n$ (for odd $n$)

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