Question

The composition of a fixedpoint-free automorphisms with conjugation is again fixedpoint-free

score 81 · Answer 1 · 2017-12-28 16:53:11

81

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The composition of a fixedpoint-free automorphisms with conjugation is again fixedpoint-free

Published on 28 Dec 2017 - 16:53

score 32 · Answer 2 · 2017-12-30 07:20:55

32

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Who can find a necessary and suficient condition on an positive integer $n$, making $Aut\mathbb{Z}_{n+1}=\mathbb{Z}_{n}$?

Published on 30 Dec 2017 - 7:20

score 117 · Answer 3 · 2017-12-30 09:55:44

117

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Automorphisms of $P/Φ(P)$ induced by those of $P$

Published on 30 Dec 2017 - 9:55

score 36 · Answer 4 · 2018-01-08 20:03:20

36

Views

How to show that $N(\varphi (a) ) = \varphi (N(a))$, where $N(b) = \{ x \in G | xb = bx \}$ is the normalizer of $b$ in $G$?

Published on 08 Jan 2018 - 20:03

score 96 · Answer 5 · 2018-01-11 04:54:49

96

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Let $G$ be a group where $|G|=p^2q$, such that $p,q$ are prime and $q\nmid Aut(G)$ then $G$ is abelian

Published on 11 Jan 2018 - 4:54

score 1.1k · Answer 6 · 2010-08-16 19:58:20

1.1k

Views

Solving $|\operatorname{Aut}(H)|=|\operatorname{Aut}(G)|$

Published on 16 Aug 2010 - 19:58

score 2.5k · Answer 7 · 2010-11-04 15:43:05

2.5k

Views

Automorphism of $S_4$

Published on 04 Nov 2010 - 15:43

score 4k · Answer 8 · 2011-03-15 15:18:43

4k

Views

Number of automorphisms of a direct product of two cyclic $p$-groups

Published on 15 Mar 2011 - 15:18

score 2.6k · Answer 9 · 2011-03-31 08:46:02

2.6k

Views

Centralizer of $Inn(G)$ in $Aut(G)$

Published on 31 Mar 2011 - 8:46

score 7.8k · Answer 10 · 2011-04-16 03:09:29

7.8k

Views

Showing that a cyclic automorphism group makes a finite group abelian

Published on 16 Apr 2011 - 3:09

score 1.6k · Answer 11 · 2011-05-19 15:40:51

1.6k

Views

Cyclic Automorphism group

Published on 19 May 2011 - 15:40

score 329 · Answer 12 · 2011-12-23 21:32:06

329

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Does there exist a group without automorphisms such that...

Published on 23 Dec 2011 - 21:32

score 2.3k · Answer 13 · 2012-02-13 16:10:18

2.3k

Views

Upper bounds on the size of $\operatorname{Aut}(G)$

Published on 13 Feb 2012 - 16:10

score 1.4k · Answer 14 · 2012-05-03 07:11:50

1.4k

Views

Give a connected graph whose automorphism group has size 3

Published on 03 May 2012 - 7:11

score 8k · Answer 15 · 2012-06-03 07:06:34

8k

Views

A characteristic subgroup is a normal subgroup

Published on 03 Jun 2012 - 7:06

List Question

The composition of a fixedpoint-free automorphisms with conjugation is again fixedpoint-free

Who can find a necessary and suficient condition on an positive integer $n$, making $Aut\mathbb{Z}_{n+1}=\mathbb{Z}_{n}$?

Automorphisms of $P/Φ(P)$ induced by those of $P$

How to show that $N(\varphi (a) ) = \varphi (N(a))$, where $N(b) = \{ x \in G | xb = bx \}$ is the normalizer of $b$ in $G$?

Let $G$ be a group where $|G|=p^2q$, such that $p,q$ are prime and $q\nmid Aut(G)$ then $G$ is abelian

Solving $|\operatorname{Aut}(H)|=|\operatorname{Aut}(G)|$

Automorphism of $S_4$

Number of automorphisms of a direct product of two cyclic $p$-groups

Centralizer of $Inn(G)$ in $Aut(G)$

Showing that a cyclic automorphism group makes a finite group abelian

Cyclic Automorphism group

Does there exist a group without automorphisms such that...

Upper bounds on the size of $\operatorname{Aut}(G)$

Give a connected graph whose automorphism group has size 3

A characteristic subgroup is a normal subgroup

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