Related papers: Automorphism groups of endomorphism semigroups of …

We show that for any $n$-ary group $(G,f)$, the group $Aut(G,f)$ can be embedded in $Aut(\mathbb{Z}_{n-1}\ltimes G)$ and so we can obtain a class of interesting automorphisms of cyclic extensions.

Let $k$ be an algebraically-closed field, and let $B = kQ/I$ be a basic, finite-dimensional associative $k$-algebra with $n := \dim_kB < \infty$. Previous work shows that the collection of maximal subalgebras of $B$ carries the structure of…

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

We study authomorphisms of $Ind$-groups of polynomial automorphisms (wich are singular) via tame approximations. Such objects were pioneeered in research by B.I.Plotkin We obtain a number of properties of $Aut(Aut(A))$, where $A$ is the…

Let $X$ be a variety of dimension $n$, and let $\mathrm{Aut}(X)$ be its automorphism group. When $X$ is quasi-affine, we prove that a solvable subgroup of $\mathrm{Aut}(X)$ that is generated by an irreducible family of automorphisms…

The group of automorphisms of the Brandt $\lambda^0$-extension $B^0_\lambda(S)$ of an arbitrary monoid $S$ with zero is described. In particular we show that the group of automorphisms $\mathbf{Aut}(B_{\lambda}^0(S))$ of $B_{\lambda}^0(S)$…

It is proved that the free $m$-generated Burnside groups $\Bbb{B}(m,n)$ of exponent $n$ are infinite provided that $m>1$, $n\ge2^{48}$.

We study the cluster automorphism group $Aut(\mathcal{A})$ of a coefficient free cluster algebra $\mathcal{A}$ of finite type. A cluster automorphism of $\mathcal{A}$ is a permutation of the cluster variable set $\mathscr{X}$ that is…

Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear iff G is a virtually nilpotent group.

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…

Let $F_n$ be the free group on $n \geq 2$ generators. We show that for all $1 \leq m \leq 2n-3$ (respectively for all $1 \leq m \leq 2n-4$) there exists a subgroup of $\operatorname{Aut}(F_n)$ (respectively $\operatorname{Out}(F_n)$) which…

We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.

For $\beta\in{\mathbb Z}$, let $G(\beta)=\langle A,B\,|\, A^{[A,B]}=A,\, B^{[B,A]}=B^\beta\rangle$ be the infinite Macdonald group, and set $C=[A,B]$. Then $G(\beta)$ is a nilpotent polycyclic group of the form $\langle…

For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…

It is proved that the semigroups $\mathrm{\mathbf{End}}(\boldsymbol{B}_{\omega})$ and $\mathrm{\mathbf{End}}(\boldsymbol{B}_{\mathbb{Z}})$ of the endomorphisms of the bicyclic semigroup $\boldsymbol{B}_{\omega}$ and the endomorphisms of the…

In this paper, we explore a variety of finiteness questions for preperiodic points of morphisms. We begin by treating a group action analog of the Burnside problem for torsion groups using the p-adic arc method. We then prove some results…

Let $A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative automorphisms $Aut(F_n;A_1,...,A_k)$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The…

Let $\mathcal M$ be a compact complex supermanifold. We prove that the set $\mathrm{Aut}_{\bar 0}(\mathcal M)$ of automorphisms of $\mathcal M$ can be endowed with the structure of a complex Lie group acting holomorphically on $\mathcal M$,…

Let $G$ be a finite group and $M,N$ be two normal subgroups of $G$. Let $Aut_N^M(G)$ denote the group of all automorphisms of $G$ which fix $N$ element wise and act trivially on $G/M$. Let $n$ be a positive integer. In this article we have…

For every positive integer $n$, we construct, using algebraic groups, an infinite family of irreducible algebraic varieties $X$,whose automorphism group ${\rm Aut}(X)$ contains the automorphism group ${\rm Aut}(F_n)$ of a free group $F_n$…