Comeagre conjugacy classes and free products with amalgamation

Free Products with Amalgamation and 3-manifolds

COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS

Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...

Products of Conjugacy Classes in Finite and Algebraic Simple Groups

We prove the Arad–Herzog conjecture for various families of finite simple groups — if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are nontrivial conjugacy classes, either both semisimple or both unipotent, then AB is not a conjugacy class. We also prove a strong version of the Arad–Herzog co...

Products of Conjugacy Classes and Fixed Point Spaces

Note that the hypothesis that V has no two-dimensional composition factors is vacuous if the characteristic of k is not 2. For our intended subsequent application it is critical that the g ∈ G that we choose does not depend on V . We also prove a variant of the previous corollary for direct products of finite simple groups. If V is a G-module, let CV (g) denote the fixed space for g ∈ G. We use...

The Geometry of Twisted Conjugacy Classes in Wreath Products

We give a geometric proof based on recent work of Eskin, Fisher and Whyte that the lamplighter group Ln has infinitely many twisted conjugacy classes for any automorphism φ only when n is divisible by 2 or 3, originally proved by Gonçalves and Wong. We determine when the wreath product G o Z has this same property for several classes of finite groups G, including symmetric groups and some nilpo...