List questions from automorphism-group

Published on 02 May 2020 - 14:02

79

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Why $G/F(G)$ is isomorphic to a subgroup of $\mathrm{Out}(F(G))$?

Published on 02 May 2020 - 16:07

311

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The automorphism of splitting field of x^p-x+a over Z_p.

Published on 26 Mar 2026 - 17:50

114

Views

Why does every $\varphi: K \to \mathrm{Out}(H)$ determine an unique extension of $H$ by $K$ when $Z(H) = 1$?

Published on 25 Mar 2026 - 12:34

173

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Frattini subgroup of $p$-groups and the automorphisms

Published on 25 Mar 2026 - 6:03

228

Views

How do automorphisms of a group act on the set of irreducible representations?

Published on 06 May 2020 - 17:33

369

Views

The direct product of quotients is a quotient of the direct product

Published on 26 Mar 2026 - 16:10

249

Views

Permutations of a subset of combinations

Published on 07 May 2020 - 12:53

281

Views

Showing that $Aut(S_n)=S_n$ for $n>6$ with a argument of centralizers.

Published on 09 May 2020 - 0:47

650

Views

Showing that there exists an automorphism of a cyclic group mapping a generator to another.

Published on 10 May 2020 - 23:01

59

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About the order of an automorphism

Published on 14 May 2020 - 18:42

84

Views

Conditions imposed on graph automorphism leave the "voltage" on graph nodes identical?

Published on 19 May 2020 - 0:19

109

Views

$G/F(G)$ is isomorphic to $X_1\times\cdots\times X_t$

Published on 25 Mar 2026 - 8:12

178

Views

Q about torus automorphism example

Published on 25 Mar 2026 - 3:24

470

Views

Is Aut(G×H) isomorphic to Aut(G) × Aut(H)

Published on 26 Mar 2026 - 17:35

List Question

Is $\mathrm{Aut}$ a functor/invariant?

Why $G/F(G)$ is isomorphic to a subgroup of $\mathrm{Out}(F(G))$?

The automorphism of splitting field of x^p-x+a over Z_p.

Why does every $\varphi: K \to \mathrm{Out}(H)$ determine an unique extension of $H$ by $K$ when $Z(H) = 1$?

Frattini subgroup of $p$-groups and the automorphisms

How do automorphisms of a group act on the set of irreducible representations?

The direct product of quotients is a quotient of the direct product

Permutations of a subset of combinations

Showing that $Aut(S_n)=S_n$ for $n>6$ with a argument of centralizers.

Showing that there exists an automorphism of a cyclic group mapping a generator to another.

About the order of an automorphism

Conditions imposed on graph automorphism leave the "voltage" on graph nodes identical?

$G/F(G)$ is isomorphic to $X_1\times\cdots\times X_t$

Q about torus automorphism example

Is Aut(G×H) isomorphic to Aut(G) × Aut(H)

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