Related papers: A note on separability in outer automorphism group…

We provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We also prove…

Johnson and Livingston have characterized peripheral structures in homomorphs of knot groups. We extend their approach to the case of links. The main result is an algebraic characterization of all possible peripheral structures in certain…

The main theorem of this document emulates, in the context of Out(F_r) theory, a mapping class group theorem (by H. Masur and J. Smillie) that determines precisely which index lists arise from pseudo-Anosov mapping classes. Since the ideal…

We first show that the moniod of separable surjective self morphisms of a variety of Ueno type coincides with the group of automorphisms. We also give an explicit description of the automorphism group. As applications, we confirm Kawaguchi…

Hahn groups endowed with the canonical valuation play a fundamental role in the classification of valued abelian groups. In this paper we study the group of valuation (respectively order) preserving automorphisms of a Hahn group $G$. Under…

Let $G$ be a finitely generated malabelian group, let $A\leq\mathrm{Out}(G)$ be a finitely generated subgroup, and let $\Gamma_{G,A}$ denote the preimage of $A$ in $\mathrm{Aut}(G)$. We give a general criterion for the linearity of…

In 1911, Burnside asked whether or not there exist groups that have an outer automorphism which preserves conjugacy classes. Two years later he answered his own question by constructing a family of such groups. Using the small group library…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…

Rosenmann and Ventura asked "What is the right definition of dependence of subgroups for general groups?". Here we aim to answer this question. We consider a definition of subgroup independence which is a special case of a…

It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group automorphisms that can be coherently extended along any outgoing homomorphism. One is thus motivated to…

A very explicit analytic formula of the separability criterion of two-party Gaussian systems is given. This formula is compared to the past formulation of the separability criterion of continuous variables two-party Gaussian systems.

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.

Let $X$ be a compact Riemann surface of genus $g\geq 2$. Let $Aut(X)$ be its group of automorphisms and $G\subseteq Aut(X)$ a subgroup. Sharp upper bounds for $|G|$ in terms of $g$ are known if $G$ belongs to certain classes of groups, e.g.…

An infinite linearly ordered set (S,<=) is called doubly homogeneous if its automorphism group A(S) acts 2-transitively on it. We show that any group G arises as outer automorphism group G cong Out(A(S)) of the automorphism group A(S), for…

In this paper, we introduce notions of partitionability and characteristic sets of homogeneous polynomials and give a complete classification of groups faithfully acting on smooth cubic fivefolds. Specifically, we prove that there exist 20…

We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgroups are finitely generated, and they satisfy a dichotomy…

In this paper we prove criteria for a nonnormal toric variety to be flexible, to be rigid and to be almost rigid. For rigid and almost rigid toric varieties we describe the automorphism group explicitly.

An $S$-ring (a Schur ring) is said to be separable with respect to a class of groups $\mathcal{K}$ if every algebraic isomorphism from the $S$-ring in question to an $S$-ring over a group from $\mathcal{K}$ is induced by a combinatorial…