All Questions
14 questions
1
vote
1
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A question about automorphism group of abelian group
Does anyone know any references that describe automorphism group $\operatorname{Aut}(\mathbb R^n\times \mathbb T^m)$? I searched for a long time but couldn't find it.
- 71
2
votes
1
answer
554
views
Growth rate of an outer automorphism of a free product
$\DeclareMathOperator\Out{Out}$Let $G=G_1\ast\cdots\ast G_k\ast F_p$ be a Grushko decomposition of a finitely generated group $G$, $\mathcal{O}$ the outer space relative to this decomposition, $[\phi]\...
- 257
2
votes
0
answers
135
views
English translation of Fouxe-Rabinovitch paper
Is there somewhere an english translation of Fouxe-Rabinovitch's papers
"D. I. Fouxe-Rabinovitch, Uber die Automorphismengruppen ¨
der freien Produkte. II, Rec. Math. [Mat. Sbornik] N.S., 1941,
...
- 257
13
votes
1
answer
1k
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Is there a name of semidirect product of a group with its automorphism group?
Consider the construction $G \rtimes \text{Aut}(G)$. Here $
G$ is a group, $\text{Aut}(G)$ is the automorphism group and the semidirect product is over the most obvious action.
1) Is there any name ...
- 885
4
votes
0
answers
236
views
Groups inducing edge-colorings on graphs. Is this concept known?
Are the following concepts known in graph/group theory, and if Yes, what are they called and where to read about them? Because I do not know better, I gave them placeholder names for now.
1. ...
- 13.6k
10
votes
1
answer
534
views
The Tits alternative for $\operatorname{Out}(F_n)$
Not sure if this is the right place to ask this, but the paper I am reading seems to be too specialised for mathstack (if you do not agree, pleas let me know and I will take down this question)
I am ...
- 275
3
votes
2
answers
337
views
Frobenius Groups of Automorphisms
Recently, I am looking different papers on the topic
$$\mbox{Frobenius groups of automorphisms of a group.}$$
But I am familiar with Frobenius groups only; not with their (faithful) actions on groups. ...
- 261
1
vote
2
answers
742
views
Automorphism group of the affine groups AGL(n,q), ASL(n,q)
I have a question. The automorphism group of the linear groups $GL(n,q)$, the group of linear transformations of $V = \mathbb{F}_q^n$, and $SL(n,q)$, the subgroup of $GL(n,q)$ consisting of elements ...
- 731
5
votes
2
answers
440
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Condition(s) for the full autormophism group $\operatorname{Aut}(C(G, S))$ of the Cayley graph of $G$ to be isomorphic to $G$
If $\Gamma = C(G, S)$ is the (undirected) Cayley graph of a finite group $G$ with generating set $S$, then $G \le \operatorname{Aut}(\Gamma)$, the "full" automorphism group of $\Gamma$.
When is it ...
- 178
3
votes
2
answers
1k
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A structure of the group of automorphisms of an infinite binary tree
My friend asked me to ask his question here. Where he can find (a paper or a book) containing a complete description (with the proof) of a structure of the group of automorphisms of an infinite binary ...
- 5,409
6
votes
4
answers
596
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Is the conjugacy problem solvable in $Out(F_n)$?
There is a paper of Martin Lustig on his webpage giving a positive answer to the conjugacy problem for the outer automorphism group of the free group $F_n$. On the other hand, there seems not to be a ...
- 12.1k
9
votes
1
answer
3k
views
Automorphism group of a finite group
I would like to ask if there exists an explicit description of $\mathrm{Aut}(G)$, the group of automorphisms of a finite group $G$, in particular, when $G$ is abelian. E.g., if $G = \mathbb{Z}/m\...
- 675
4
votes
1
answer
1k
views
Automorphism group of factor groups
Let $G$ be a group and let $H$ be a factor group of $G$. Is there any result that relates $\operatorname{Aut}(G)$ (the automorphism group of $G$) and $\operatorname{Aut}(H)$?
As a very special case ...
- 1,108
5
votes
2
answers
984
views
Automorphism Group of some Classical groups
Hi All,
I would like to know the Automorphism group of some simple classical groups, such as PSL(n,q) or some PSU or PSp groups. Could you please give me some recommended books or papers then? I ...
- 233