* Supported by a grant from the Graduiertenkolleg " Analyse und Konstruktion in der Mathematik " , RWTH Aachen.

In this paper we introduce the graph Γsc(G) associated with a group G, called solvable conjugacy class (abbreviated as SCC-graph), whose vertices are nontrivial classes of G and two distinct C,D adjacent if there exist x∈C y∈D such that 〈x,y〉 is solvable. We discuss connectivity, girth, clique number, several other properties SCC-graph. One our results asserts only finitely many finite groups S...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction o...

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...

We define a Rohlin property for actions of Z on UHF algebras and show a noncommutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. In particular we present two classes of UHF algebras. For UHF algebras in one class, which includes the CAR algebra, there is one and only one outer conjugacy class of product type action...

The known algorithms for solving the conjugacy problem in Garside groups involve computing a particular subset of the conjugacy class, the so-called super summit set. The super summit set [g] of an element g in a Garside group is, intuitively, the set of all conjugates of g that have the shortest normal form in the conjugacy class of g. In this paper, we define the stable super summit set [g] o...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction o...

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by ∼p, ∼o, and ∼c) in certain classes of finitely presented monoids. We will show that in the class of polycyclic monoids, p-conjugacy is “almost” transitive, ∼c is stric...

We give examples of analytic circle maps with singularities of break type with the same rotation number and the same size of the break for which no conjugacy is Lipschitz continuous. In the second part of the paper, we discuss a class of rotation numbers for which a conjugacy is C1-smooth, although the numbers can be strongly non-Diophantine (Liouville). For the rotation numbers in this class, ...