We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some ex...

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...

‎the purpose of this paper is the determination of the inertia‎ ‎factors‎, ‎the computations of the fischer matrices and the ordinary‎ ‎character table of the split extension $overline{g}=‎ ‎3^{7}{:}sp(6,2)$ by means of clifford-fischer theory‎. ‎we firstly‎‎determine the conjugacy classes of $overline{g}$ using the coset‎ ‎analysis method‎. ‎the determination of the inertia factor groups of‎ ‎...

Abstract In this paper we characterize, in terms of their conjugacy classes, linear groups G such that $$G/\zeta _k(G)$$ G / ζ k ( ) belongs to a certain group class $$\mathfrak {...

results of Hagedorn gave me the courage to attempt such calculations for general groups and to obtain closed multiplicity formulas for orthogonal groups. It is a pleasure to thank Dick Gross for initiating the work in [12] which led to this paper, for helpful remarks on an earlier version, and for aquainting me with Hagedorn’s thesis. The referee read the original version of this paper with car...

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...

Let G be P SL n (q); P SU n (q); Sp 2n (q) or P Sp 2n (q), where q is a power of the prime p. Using results on the numbers of special squarefree polynomials over nite elds, we describe and count the conjugacy classes of p 0-elements with abelian centralizers in G. Similar results are obtained for the semisimple orbits of G on the corresponding nite Lie algebras.

Let Mod(Sg) be the mapping class group of closed orientable surface Sg genus g?1. In this paper, we develop various methods for factoring periodic classes into Dehn twists, up to conjugacy. As applications, certain roots twists as words in twists. We will also show existence conjugates maps order 4g and 4g+2, g?2, whose product is pseudo-Anosov.

We study a Poisson structure π on the Grothendieck resolution X of a complex semi-simple group G and prove that the desingularization map μ : (X,π)→ (G,π0) is Poisson, where π0 is a Poisson structure such that intersections of conjugacy classes and opposite Bruhat cells BwB− are Poisson subvarieties. We compute the symplectic leaves of X and show that (X,π) resolves singularities of (G,π0).