Related papers: Class preserving automorphisms of unitriangular gr…

It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of the Cuntz algebra O_n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via…

Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension…

We characterize all finite p-groups G of order p^n(n\leq 6), where p is a prime for n\leq 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.

Let $n$ and $k$ be integers with $n>2k, k\geq1$. We denote by $H(n, k)$ the $bipartite\ Kneser\ graph$, that is, a graph with the family of $k$-subsets and ($n-k$)-subsets of $[n] = \{1, 2, ... , n\}$ as vertices, in which any two vertices…

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli stack parametrizing Deligne-Mumford stable $n$-pointed genus $g$ curves and let $\overline{M}_{g,n}$ be its coarse moduli space: the Deligne-Mumford compactification of the moduli space of…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

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.

For any right-angled Artin group $A_{\Gamma}$, Charney--Stambaugh--Vogtmann showed that the subgroup $U^0(A_{\Gamma}) \leq\text{Out}(A_{\Gamma})$ generated by Whitehead automorphisms and inversions acts properly and cocompactly on a…

Let $G_n=\mathbb{Z}_n\times \mathbb{Z}_n$ for $n\geq 4$ and $S=\{(i,0),(0,i),(i,i): 1\leq i \leq n-1\}\subset G_n$. Define $\Gamma(n)$ to be the Cayley graph of $G_n$ with respect to the connecting set $S$. It is known that $\Gamma(n)$ is a…

Let $\Out(F_n)$ denote the outer automorphism group of the free group $F_n$ with $n>3$. We prove that for any finite index subgroup $\Gamma<\Out(F_n)$, the group $\Aut(\Gamma)$ is isomorphic to the normalizer of $\Gamma$ in $\Out(F_n)$. We…

Let $\sigma$ be an automorphism of a field $K$ with fixed field $F$. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras $K[t;\sigma]/fK[t;\sigma]$ obtained…

Let $\mathbb{K}$ be the algebraic closure of a finite field $\mathbb{F}_q$ of odd characteristic $p$. For a positive integer $m$ prime to $p$, let $F=\mathbb{K}(x,y)$ be the transcendency degree $1$ function field defined by…

In this paper we focus on the description of the automorphism group $\Gamma_{\parallel}$ of a Clifford-like parallelism $\parallel$ on a $3$-dimensional projective double space…

Let $G\subset GL_n(k)$ be a finite subgroup and $k[x_1,\dots, x_n]^G\subset k[x_1,\dots, x_n]$ its ring of invariants. We show that, in many cases, the automorphism group of $k[x_1,\dots, x_n]^G$ is $k^\times$. Version 2: Incorporates parts…

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…

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…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…

Let $\Gamma_g$ be the fundamental group of a closed orientable surface of genus $g\geqslant 2$. The outer automorphism group $\mathrm{Out}(\Gamma_g)$ naturally acts on the character variety $\mathcal{X}(\Gamma_g,G)$ for any Lie group $G$.…

A quantum graph $\mathcal{G}$ housed by a matrix algebra $M_n$ can be encoded as an operator system $\mathcal S=\mathcal{S}_{\mathcal{G}}\le M_n$. There are two sensible notions of quantum automorphism group for any such:…

An endomorphism of a free group is called primitivity preserving if it takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank n > 2 is an…