List questions from automorphism-group

Published on 28 Dec 2015 - 13:46

394

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algebraic closure is the intersection of all elementary sub-models of the monster

Published on 03 Feb 2016 - 16:05

438

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If an automorphism sends more than half of the elements to themselves then it's the identity

Published on 25 Mar 2016 - 14:29

2.4k

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Automorphism of a group of integer is isomorphic to U(n)

Published on 07 Apr 2016 - 2:52

576

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Groups which can not occur as automorphism group of a group

Published on 18 Apr 2016 - 10:22

7.3k

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Find $Aut(Z_{6})$

Published on 28 Mar 2026 - 17:14

158

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The automorphism of a group when given a group presentation

Published on 26 Mar 2026 - 21:54

5.7k

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Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.

Published on 18 May 2013 - 14:53

164

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Why if $\phi\in\mathrm{Aut}(L)$ and $x\in L$ then $\phi(\operatorname{ad} x)\phi^{-1}=\operatorname{ad}\phi(x)$?

Published on 12 Aug 2013 - 6:58

1.2k

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Automorphism group of alternating group.

Published on 19 Sep 2013 - 10:53

1.5k

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The automorphism group of the complete binary rooted tree of height $3$

Published on 12 Nov 2013 - 17:48

1.4k

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Show that if $ \gcd(|G|,|H|) = 1 $, then $ \text{Aut}(G \times H) \cong \text{Aut}(G) \times \text{Aut}(H) $.

Published on 30 Nov 2013 - 5:45

4.4k

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Automorphism group of ${\bf Z}_p$

Published on 03 Jan 2014 - 7:55

5.6k

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When is the automorphism group $\text{Aut }G$ cyclic?

Published on 30 Jan 2014 - 13:54

206

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Prove the automorphism preserves the relation among roots.

Published on 11 May 2017 - 1:36

List Question

Why $\operatorname{Aut}(A_5 )$ is isomorphic to $ S_5$?

algebraic closure is the intersection of all elementary sub-models of the monster

If an automorphism sends more than half of the elements to themselves then it's the identity

Automorphism of a group of integer is isomorphic to U(n)

Groups which can not occur as automorphism group of a group

Find $Aut(Z_{6})$

The automorphism of a group when given a group presentation

Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.

Why if $\phi\in\mathrm{Aut}(L)$ and $x\in L$ then $\phi(\operatorname{ad} x)\phi^{-1}=\operatorname{ad}\phi(x)$?

Automorphism group of alternating group.

The automorphism group of the complete binary rooted tree of height $3$

Show that if $ \gcd(|G|,|H|) = 1 $, then $ \text{Aut}(G \times H) \cong \text{Aut}(G) \times \text{Aut}(H) $.

Automorphism group of ${\bf Z}_p$

When is the automorphism group $\text{Aut }G$ cyclic?

Prove the automorphism preserves the relation among roots.

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