List questions from automorphism-group

Published on 29 Mar 2026 - 5:34

17

Views

Deg of extension of Q equals number of automorphisms times distinct images in C

Published on 20 Dec 2021 - 17:15

99

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Under what conditions can we say that $G/N \cong S \implies G \cong N \times S$?

Published on 28 Mar 2026 - 18:17

138

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Non-trivial automorphisms that fix maximal subgroups?

Published on 25 Mar 2026 - 15:39

265

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What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity?

Published on 25 Mar 2026 - 7:48

42

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Subfield fixed points and corresponding rational field

Published on 26 Dec 2021 - 14:40

76

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Generating a larger group using automorphism

Published on 01 Jan 2022 - 7:42

224

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Showing ${\rm Aut}(D_{2^n})\cong{\rm Aut}(Q_{2^n})$ for $n\ge 4$.

Published on 29 Mar 2026 - 11:49

167

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If $G$ is centerless, so is $\operatorname{Aut}(G)$

Published on 01 Jan 2022 - 23:03

57

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Automorphism Group of a Space

Published on 06 Jan 2022 - 14:10

657

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Showing ${\rm Aut}(Q_{2^n})\cong{\rm Hol}(\Bbb Z_{2^{n-1}})$ for $n>3$

Published on 23 Feb 2026 - 0:30

111

Views

Show ${\rm Aut}(G)$ is a $2$-group, where $G$ is given by a particular presentation

Published on 28 Mar 2026 - 13:28

46

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Order of ${\rm Aut}(G)$ given $G$ is abelian group of order $30$

Published on 25 Jan 2022 - 8:23

171

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Semidirect product and direct product

Published on 30 Mar 2026 - 20:24

145

Views

Please tell me how to formalize my thought if my thought is not wrong. ("obvious by symmetry", "symmetric group")

Published on 29 Jan 2022 - 7:54

List Question

Quotients of automorphism groups of finite field extensions

Deg of extension of Q equals number of automorphisms times distinct images in C

Under what conditions can we say that $G/N \cong S \implies G \cong N \times S$?

Non-trivial automorphisms that fix maximal subgroups?

What if an automorphism fixes every maximal subgroup pointwise. Is it then the identity?

Subfield fixed points and corresponding rational field

Generating a larger group using automorphism

Showing ${\rm Aut}(D_{2^n})\cong{\rm Aut}(Q_{2^n})$ for $n\ge 4$.

If $G$ is centerless, so is $\operatorname{Aut}(G)$

Automorphism Group of a Space

Showing ${\rm Aut}(Q_{2^n})\cong{\rm Hol}(\Bbb Z_{2^{n-1}})$ for $n>3$

Show ${\rm Aut}(G)$ is a $2$-group, where $G$ is given by a particular presentation

Order of ${\rm Aut}(G)$ given $G$ is abelian group of order $30$

Semidirect product and direct product

Please tell me how to formalize my thought if my thought is not wrong. ("obvious by symmetry", "symmetric group")

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