# Tagged Questions

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### Automorphisms of SO_n(k,f)

Let $k$ be a field, $n\in\mathbb{N}$ and $f:k^n\times k^n\to k$ a non-degenerate symmetric bilinear form. Let $$O_n(k,f):=\{ g\in GL_n(k) \mid \forall x,y\in k^n : f(x,y)=f(g.x,g.y) \}$$ and ...
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### $PSL_2(\mathbb{Z}/p^n)$ isomorphic to automorphism group of depth-$n$, $(p+1)$-regular tree?

A comment on another question (linked below) states "The group $PSL_2((\mathbb{Z}/p^n))$ is the automorphisms group of the $(p+1)$ regular tree of depth $n$, where at level $m$ of the tree you have ...
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### Find finite groups $G\cong Aut(G)$

I become interested in this problem because $G\cong Aut(G)$ suggests a special symmetry in $G$. From $G/Z(G)\cong Inn(G)$ we know complete group is the anewer for the simplest case, though this class ...
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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 ...
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### Iterated Automorphism Groups

Notation: For each group $G$ define: $Aut^{(0)}(G):=G$ $Aut^{(1)}(G):=Aut(G)$ $\forall n\geq 1~~~Aut^{(n+1)}(G):=Aut(Aut^{(n)}(G))$ Question: Consider $I\subseteq \omega$. Is there a group $G$ ...
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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 ...
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### What are the endomorphisms of the group of affine transformations of a field?

Let $k$ be a field (I am mostly concerned with $k=\mathbb{Q}$) and let $A$ denote the group of affine transformations of $k$. In other words $A$ is (isomorphic to) the group ...
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### Root system automorphisms as inner automorphisms of extended Chevalley group

For each automorphism $\sigma$ of a root system $\Phi$ there is a unique automorphism of the Chevalley group $G(\Phi,R)$ such that $\sigma(x_\alpha(t))=x_{\sigma\alpha}(t')$. While conjugating by ...
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### Automorphism of a wreath product

Let $S_k \wr S_n$ be the wreath product of two symmetric groups (so $S_n$ acts on $(S_k)^n = S_k \times ... \times S_k$ by permuting the factors; we then take the semi-direct product). What is ...