Related papers: Automorphism-invariant positive definite functions…

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…

In this paper, we initiate the study of palindromic automorphisms of groups that are free in some variety. More specifically, we define palindromic automorphisms of free nilpotent groups and show that the set of such automorphisms is a…

This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.

In this article, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that…

The object of this expository work is to try to unveil the topological/geometric intuition behind the theory of free groups and their automorphism and outer automorphism groups. The method we follow is to focus on a series of problems in…

This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups…

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

We first present an overview of our previous work on the dynamics of subgroups of automorphism groups of compact complex surfaces, together with a selection of open problems and new classification results. Then, we study two families of…

Using suitable convex functions, we construct a new family of flat Minkowski planes whose automorphism groups are at least $3$-dimensional. These planes admit groups of automorphisms isomorphic to the direct product of $\mathbb{R}$ and the…

This article proposes an effective criterion for lifting automorphisms along regular coverings of graphs, with the covering transformation group being any finite abelian group.

Let $F_n$ be the free group on $n\ge 2$ elements and $\A(F_n)$ its group of automorphisms. In this paper we present a rich collection of linear representations of $\A(F_n)$ arising through the action of finite index subgroups of it on…

In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…

We study the automorphism groups of free-by-cyclic groups and show these are finitely generated in the following cases: (i) when defining automorphism has linear growth and (ii) when the rank of the underlying free group has rank at most 3.…

The motivation for this paper is to extend the known model theoretic treatment of differential Galois theory to the case of linear difference equations (where the derivative is replaced by an automorphism.) The model theoretic difficulties…

We describe the full automorphism group of the directed reduced power graph and the undirected reduced power graph of a finite group. We compute the full automorphism groups of these graphs of several classes of finite groups. Also, we…

This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…

The paper is intended to be a survey on some topics within the framework of automorphisms of a relatively free groups of infinite rank. We discuss such properties as tameness, primitivity, small index, Bergman property, and so on.

This report is an account of freely representable groups, which are finite groups admitting linear representations whose only fixed point for a nonidentity element is the zero vector. The standard reference for such groups is Wolf (1967)…

In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…