Related papers: Conjugacy classes of autohomeomorphisms of $\mathb…

We describe the conjugacy classes of affine automorphisms in the group $Aut(n,\K)$ (respectively $Bir(\K^n)$) of automorphisms (respectively of birational maps) of $\K^n$. From this we deduce also the classification of conjugacy classes of…

We study, from a constructive computational point of view, the techniques used to solve the conjugacy problem in the "generic" lattice-ordered group Aut(R) of order automorphisms of the real line. We use these techniques in order to show…

We study the conjugacy problem in the automorphism group $Aut(T)$ of a regular rooted tree $T$ and in its subgroup $FAut(T)$ of finite-state automorphisms. We show that under the contracting condition and the finiteness of what we call the…

This article is concerned with conjugacy problems arising in homeomorphisms group, Hom($F$), of unbounded subsets $F$ of normed vector spaces $E$. Given two homeomorphisms $f$ and $g$ in Hom($F$), it is shown how the existence of a…

In this paper, we count the number of conjugacy and automorphism-conjugacy classes of elements of a ZM-group. The size of a conjugacy class with respect to these two equivalence relations is also counted.

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.

We prove that the conjugacy problem in Out(Fm) is solvable for the class of outer automorphisms whose restrictions to their polynomial subgroups are of finite order. To do this, we first investigate the structure of suspensions of free…

In this article, we consider the ball model of an infinite dimensional complex hyperbolic space, i.e. the open unit ball of a complex Hilbert space centered at the origin equipped with the Caratheodory metric. We consider the group of…

We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…

The conjugacy classes of the involutive automorphisms of the affine Kac-Moody algebras \Cli\ for $\ell\geq 2$ are determined using the matrix formulation of automorphisms of an affine Kac-Moody algebra.

Let $G$ be a finite $p$-group such that $x\Z(G) \subseteq x^G$ for all $x \in G- \Z(G)$, where $x^G$ denotes the conjugacy class of $x$ in $G$. Then $|G|$ divides $|\Aut(G)|$, where $\Aut(G)$ is the group of all automorphisms of $G$.

Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental…

We survey, and extend, results on the adjoint action of the homeomorphism group $H(X)$ on the space of surjective continuous maps, $C_s(X)$, where $X$ is a Cantor set. We look also at the restriction of the action to various dynamically…

In the group of polynomial automorphisms of the plane, the conjugacy class of an element is closed if and only if the element is diagonalisable. In this article, we show that this does not hold for the group of special automorphisms, giving…

The trialitarian automorphisms considered in this paper are the outer automorphisms of order 3 of adjoint classical groups of type D_4 over arbitrary fields. A one-to-one correspondence is established between their conjugacy classes and…

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

Many non-locally compact second countable groups admit a comeagre conjugacy class. For example, this is the case for the automorphism group of the rational order and the automorphism group of the random graph [Truss]. A. Kechris and C.…

We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the…

We study the conjugacy classes of the classical affine groups. We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups. We use these to get good upper bounds for the…

We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product…