Question

Problem $3E.1$ from Isaacs's "Finite group theory".

score 154 · Answer 1 · 2022-09-10 19:59:03

154

Views

Problem $3E.1$ from Isaacs's "Finite group theory".

Published on 10 Sep 2022 - 19:59

score 70 · Answer 2 · 2022-09-12 19:11:24

70

Views

Why if $H_5$ acts on $H_{17}$ by conjugation, this means that $5$ should divide $16$?

Published on 12 Sep 2022 - 19:11

score 33 · Answer 3 · 2022-09-18 12:51:14

33

Views

Question 10.1.6 (A course in the theory of groups, Robinson D.)

Published on 18 Sep 2022 - 12:51

score 85 · Answer 4 · 2022-09-23 08:10:04

85

Views

Does $\mathbb Z_k \leqslant H$ imply $\operatorname{Aut}(\mathbb Z_k) \leqslant \operatorname{Aut}(H)$ for some $k > 2$?

Published on 23 Sep 2022 - 8:10

score 177 · Answer 5 · 2022-10-03 17:46:17

177

Views

How many automorphisms

Published on 03 Oct 2022 - 17:46

score 80 · Answer 6 · 2022-10-05 15:06:40

80

Views

What implications does the outer automorphism of $S_6$ have in the algebra of rational, real, or complex numbers?

Published on 05 Oct 2022 - 15:06

score 195 · Answer 7 · 2022-10-06 15:34:45

195

Views

Is there any nontrivial group that is isomorphic to its outer automorphism group?

Published on 06 Oct 2022 - 15:34

score 43 · Answer 8 · 2022-10-07 10:03:08

43

Views

Morphisms between $\mathbf{GL}_2(\mathbb{Z})$ and $\mathbf{GL}_2(\mathbb{Q})$

Published on 07 Oct 2022 - 10:03

score 75 · Answer 9 · 2022-10-13 17:01:45

75

Views

If $\sigma(\alpha)$ takes finitely many values when $ \sigma$ runs over automorphism (as field) of $ \Bbb{C}$, why $ \alpha$ is algebraic number?

Published on 13 Oct 2022 - 17:01

score 216 · Answer 10 · 2022-10-14 01:44:35

216

Views

Dummit and Foote: conjugate elements and conjugate subgroups have the same order.

Published on 14 Oct 2022 - 1:44

score 65 · Answer 11 · 2022-10-14 03:04:23

65

Views

If $H\cong Z_2$, then $\text{Aut}(H)=1$.

Published on 14 Oct 2022 - 3:04

score 99 · Answer 12 · 2026-02-23 15:14:32

99

Views

What does 'Isogeny is determined by its kernel up to automorphisms' mean?

Published on 23 Feb 2026 - 15:14

score 43 · Answer 13 · 2022-10-19 10:32:05

43

Views

Galois group of $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Published on 19 Oct 2022 - 10:32

score 53 · Answer 14 · 2026-03-29 18:30:25

53

Views

Automorphism of the following rational function

Published on 29 Mar 2026 - 18:30

score 124 · Answer 15 · 2022-10-28 10:01:00

124

Views

If $\phi\in\mathsf{Aut}(G)$ fixes conjugacy classes and $G$ is finite then do we have $\phi\in\mathsf{Inn}(G)$?

Published on 28 Oct 2022 - 10:01

List Question

Problem $3E.1$ from Isaacs's "Finite group theory".

Why if $H_5$ acts on $H_{17}$ by conjugation, this means that $5$ should divide $16$?

Question 10.1.6 (A course in the theory of groups, Robinson D.)

Does $\mathbb Z_k \leqslant H$ imply $\operatorname{Aut}(\mathbb Z_k) \leqslant \operatorname{Aut}(H)$ for some $k > 2$?

How many automorphisms

What implications does the outer automorphism of $S_6$ have in the algebra of rational, real, or complex numbers?

Is there any nontrivial group that is isomorphic to its outer automorphism group?

Morphisms between $\mathbf{GL}_2(\mathbb{Z})$ and $\mathbf{GL}_2(\mathbb{Q})$

If $\sigma(\alpha)$ takes finitely many values when $ \sigma$ runs over automorphism (as field) of $ \Bbb{C}$, why $ \alpha$ is algebraic number?

Dummit and Foote: conjugate elements and conjugate subgroups have the same order.

If $H\cong Z_2$, then $\text{Aut}(H)=1$.

What does 'Isogeny is determined by its kernel up to automorphisms' mean?

Galois group of $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Automorphism of the following rational function

If $\phi\in\mathsf{Aut}(G)$ fixes conjugacy classes and $G$ is finite then do we have $\phi\in\mathsf{Inn}(G)$?

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