We show that every two-dimensional class of topological similarity, and hence every diagonal conjugacy class of pairs, is meager in the group of order preserving bijections of the rationals and in the group of automorphisms of the ordered rational Urysohn space.

This paper introduces the concept of Artin semigroup a large (extra large) type. We prove their injective embedding in corresponding groups type and solvability word conjugacy problem this class semigroups.

We define a notion of effectiveness for subshifts on finitely generated groups. The set of effective subshifts forms a conjugacy class that contains the class of sofic subshifts. We prove that the inclusion is strict for several groups, including amenable groups and groups with more than two ends.

Generalizing results on spin character degrees, we determine for a given conjugacy class of odd type in the double cover of S n spin characters of S n which have the minimal 2-power on this class in their character value. Surprisingly, the Glaisher map plays an important r^ ole here.

Let G be a group. Two elements x, y are said to be in the same z-class if their centralizers are conjugate in G. The conjugacy classes give a partition of G. Further decomposition of the conjugacy classes into z-classes provides an important information about the internal structure of the group. Let V be a vector space of dimension n over a field F of characteristic different from 2. Let B be a...

We show that the conjugacy class of an eventually expanding continuous piecewise affine interval map is contained in a smooth codimension 1 submanifold of parameter space. In particular conjugacy classes have empty interior. This is based on a study of the relation between induced Markov maps and ergodic theoretical behavior. Dept. of Mathematics, Northwestern University, Evanston, IL 60208-273...

Starting from the first elementary canonical state model, the new simple state model of the thirdorder dynamical systems that belong to Class C is derived. A typical property of this new model is a very simple form of its partial transformation matrix in the conditions of linear topological conjugacy, which represents the unity matrix. Complete state equations and the corresponding integrator-b...

We analyze the structure of the frequency space Q(F ) of a nonabelian free group F = F (a1, . . . , ak) consisting of all shift-invariant Borel probability measures on ∂F and construct a natural action of Out(F ) on Q(F ). In particular we prove that for any outer automorphism φ of F the conjugacy distortion spectrum of φ, consisting of all numbers ||φ(w)||/||w||, where w is a nontrivial conjug...

We describe combinatorial techniques to determine the numbers of semisim-ple conjugacy classes and adjoint orbits with xed class of centralizers for simply connected nite groups of Lie type.

Conjugacy separability of any group of the class of one-relator groups given by the presentation a, b; a m , b n 1m, n > 1 is proven. The proof made used of theoretical combinatorial group methods, namely the structure of amalgamated free products and some properties of the subgroups and quotients of any group of the class of one-relator groups given above.