# Tagged Questions

Questions about the group of automorphisms of any mathematical object $X$ endowed with a given structure, i.e the group of all bijective maps from $X$ to itself preserving this structure, and hence helping study it further and understand it better.

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### Need help with paper written in Russian… Yorgov's paper on self-dual codes with automorphisms of odd order

I came across this paper by V.I.Yorgov named "Binary self-dual codes with automorphisms of odd order". (Actually I was first reading another paper by Borello that cited this paper. It later become ...
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### Automorphism group of a class of abelian varieties

Given two abelian varieties $V$ and $V'$ sharing the same Hasse-Weil L-function, is there a well known, 'canonical' notion of automorphism groups thereof such that $Aut(V)\cong Aut(V')$? If so, does ...
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### Size of automorphism group of random regular graph

If I pick a random regular graph on $n$-vertices and degree $d$ from uniform distribution what is the probability that its automorphism group is of size at least $m$? -- I want to know what is the ...
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### Is the restriction of a graded automorphism linearizable in characteristic zero?

This question follows up a previous one which was answered by Todd Leason. I want to impose two new requirements on the setup. Let $k$ be a characteristic zero field. Let $A=k[x_1,\dots,x_n]$ be the ...
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### Is the restriction of a graded automorphism of a polynomial ring to a polynomial subring linearizeable?

Let $k$ be a field and let $A=k[x_1,\dots,x_n]$ be a polynomial algebra over $k$, and let $B\subset A$ be a graded subalgebra that is itself a polynomial ring, i.e. $B=k[f_1,\dots,f_m]$ for some ...
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### Automorphisms of Cuntz algebra

Suppose, $O_{\infty}$ is the cuntz algebra generated by the orthogonal isometries $\{S_i\}_{i\in \mathbb{N}}$,i.e. $S_i^*S_j=\delta_{ij}$ and $O_{\infty}=C^*(\{S_i\}_{i\in \mathbb{N}})$. Then ...
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### Authomorphisms of factoralgebra A_5 over its center in characteristic 2

Let L be classical Lie algebra of type A_5 over field of characteristic 2, M - factoralgebra L/Z(L) where Z(L) - center of L. What about group of automorphisms of M? Does anybody know answer or at ...
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### 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. ...
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### On group of automorphisms of direct product of nonabelian finite groups [closed]

Let $A, B$ be finite nonabelian groups such that $(|A|, |B|) = 1$. Is $\operatorname{Aut}(A\times B) = \operatorname{Aut}(A)\times\operatorname{Aut}(B)$?
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### Automorphism group of a variety

Suppose $X$ is a (quasi-projective) variety over a field $k$, and let $\mathbb{P}^n(k)$ be the ambient projective space. When can one decide that the automorphism group of $X$ is induced by a ...
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### 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 ...
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### GIT quotients and automorphisms

Let $X$ be a smooth projective variety. Then we have an exact sequence: $$0\mapsto Aut^{o}(X)\rightarrow Aut(X)\rightarrow H\mapsto 0$$ where $Aut^{o}(X)$ and $H$ are respectively the connected ...
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### Are automorphism groups of polarized varieties of finite type

It is "well-known" that the stack of polarized varieties is an algebraic stack with quasi-compact and separated diagonal. In particular, if $(X,L)$ and $(Y,M)$ are polarized schemes over a scheme $S$,...
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### Thickening graphs to get honest actions

Let $X$ be a finite graph. Its fundamental group is the free group $F_n$ on (say) $n$ generators. Let further an automorphism $\phi$ of $F_n$ be given. It is not true in general that this ...