Abstract Let G be a simple algebraic group of adjoint type over an algebraically closed field k bad characteristic. We show that its sheets conjugacy classes are parametrized by -conjugacy pairs $(M,{\mathcal O})$ where M is the identity component centralizer semisimple element in and ${\mathcal O}$ rigid unipotent class , analogy with good characteristic case.

It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed, for other generating sets, for restricted permutational wreath products of finite groups by the finitary symmetric group, and for alternating groups. Similar m...

Abstract. Let SL(2, q) be the group of 2× 2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of at least q − 1 distinct conjugacy classes of SL(2, q). On the other hand, if q > 3 is odd, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of a...

An Agol cycle is a complete invariant of the conjugacy class pseudo-Anosov mapping class. We study necessary and sufficient conditions for equivalent cycles 3-braids.

It is well known that the dynamics and conjugacy class of a complex Möbius transformation can be determined from a simple rational function of the coefficients of the transformation. We study the group of quaternionic Möbius transformations and identify simple rational functions of the coefficients of the transformations that determine dynamics and conjugacy.

The Weyl groups are important for Lie algebras. Lie algebras arise in the study of Lie groups, coming from symmetries of differential equations, and of differentiable manifolds. The Weyl groups have been used to classify Lie algebras up to isomorphism. The Weyl group associated to a Lie algebra of type Bn and the group of graph automorphisms of the n-cube Aut(Qn) are known to be isomorphic to Z...

The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys–Murphy element involves many conjugacy classes with complicated coefficients. In this article we consider a combinatorial setup which allows us to manipulate such products easily: to...

Given an automorphism of a free group Fn, we consider the following invariants: e is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); d is the maximal degree of polynomial growth of conjugacy classes; R is the rank of the fixed subgroup. We determine precisely which triples (e, d, R) may be realized by an automorphism o...

Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class g of G we define its centralizing subgroup to be HCG(g). Let K be such that H ≤ K ≤ G. We show that the G-conjugacy classes contained in K whose centralizing subgroup is K, are equally distributed between the cosets of H in K. The proof of this result is entirely elementary. As an application we fin...