Related papers: The automorphism group of the group of unitriangul…

We prove that the unitriangular automorphism group of a free group of rank $n$ has a faithful representation by matrices over a field, or in other words, it is a linear group, if and only if $n \leq 3.$ Thus, we have completed a description…

The groups of automorphisms of the Lie algebras of unitriangular polynomial derivations are found.

We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

Let $G$ be a group. The orbits of the natural action of $Aut(G)$ on $G$ are called the automorphism orbits of $G$, and their number is denoted by $\omega(G)$. Let $\mathbb{F}$ be an infinite field, and let $UT_n(\mathbb{F})$ denote the…

We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…

The description of the automorphism group of group $<a, b; [a^m,b^n]=1>$ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.

The group of automorphisms is found for the Lie algebra of polynomial vector fields with constant divergence.

The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

Let $X$ be a smooth complex projective curve, and let $x\in X$ be a point. We compute the automorphism group of the moduli space of framed vector bundles on $X$ of rank $r \geq 2$ with a framing over $x$. It is shown that this automorphism…

The groups of automorphisms of the Lie algebras of formally analytic vector fields with constant divergence are found.

We determine the automorphism group of the zero-divisor digraph of the semiring of matrices over an antinegative commutative semiring with a finite number of zero-divisors.

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.

We give upper bounds on the order of the automorphism group of a simple graph

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.