Related papers: On the Automorphisms of Some One-Relator Groups

Let $k$ be an algebraically-closed field, and $B$ a unital, associative $k$-algebra with $n := \dim_kB < \infty$. For each $1 \le m \le n$, the collection of all $m$-dimensional subalgebras of $B$ carries the structure of a projective…

We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine…

There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation…

We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.

An automorphism of a graph $G=(V,E)$ is a bijective map $\phi$ from $V$ to itself such that $\phi(v_i)\phi(v_j)\in E$ $\Leftrightarrow$ $v_i v_j\in E$ for any two vertices $v_i$ and $v_j$. Denote by $\mathfrak{G}$ the group consisting of…

Let $G$ be a graph of order $n$ and let $k\in \{1,2,\ldots,n-1\}$. The $k$-token graph of $G$ is the graph, whose vertices are all the $k$-subsets of vertices of $G$, where two such $k$-sets are adjacent whenever their symmetric difference…

We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact group $G$ is an isometric automorphism.

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.

Let $G$ be a group. The directed endomorphism graph, $\dend(G)$ of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex $a$ to the vertex $b$ if $a \neq b$ and there exists an endomorphism on $G$ mapping…

We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts ``like…

Let L be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism f of L is called normal if f(I)=I for every ideal I of the algebra L. Such automorphisms form a normal subgroup N(L)…

The goal of this paper is to construct and describe certain arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic subgroup…

In this paper we revisit the description of all verbal subgroups of the group of automorphisms of a regular rooted tree $\mathcal{T}_d$, for $d>2$ and odd.

We study the automorphism group of the algebra $\oqmn$ of $n \times n$ generic quantum matrices. We provide evidence for our conjecture that this group is generated by the transposition and the subgroup of those automorphisms acting on the…

A binary operation on any set induces a binary operation on its subsets. We explore families of subsets of a group that become a group under the induced operation and refer to such families as power groups of the given group. Our results…

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

We conjecture a characterization of a cluster automorphism as an algebra homomorphism from the cluster algebra to itself that restricts to a bijection between two clusters. This formulation does not require that the map commutes with…

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

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

In this paper we prove that every automorphism of a Chevalley group (or its elementary subgroup) with root system of rank >1 over a commutative ring (with 1/2 for the systems A_2, F_4, B_l, C_l; with 1/2 and 1/3 for the system G_2) is…