We present explicit upper bounds for the number and size of conjugacy classes in finite
Chevalley groups and their variations. These results have been used by many authors to …

ON THE COMMUTING PROBABILITY IN FINITE GROUPS For Bernd Fischer on the occasion
of his 70th birthday Introduction: When G is af Page 1 ON THE COMMUTING PROBABILITY IN …

The importance of conjugacy classes for the structure of finite groups was recognised very
early in the study of groups. In this survey we consider the results from the many articles …

We present two analogues of two well-known elementary arguments for a lower bound for p
(n), the number of partitions of the integer n. One of these is character-theoretic, and the …

The k (GV) conjecture claims that the number of conjugacy classes (irreducible characters)
of the semidirect product GV is bounded above by the order of V. Here V is a finite vector …

The commutativity degree of a group is the probability that two randomly selected (with
replacement) elements of the group commute. We find bounds on the commutativity degree …

Let k (H) denote the number of conjugacy classes of a finite group H. In this paper we
address the following problem. Problem 1.1. Assume a finite group H has a normal …

Let G be a finite group. Denote by Irr (G) the set of all irreducible complex characters of G.
Let\rm cd (G)={χ (1)\;|\; χ ∈\rm Irr (G)\} be the set of all irreducible complex character degrees …

Let V be a finite faithful completely reducible FG-module for a finite field F and a finite group
G. In various cases explicit linear bounds in| V| are given for the numbers of conjugacy …

A rack of order $ n $ is a binary operation $\rack $ on a set $ X $ of cardinality $ n $, such
that right multiplication is an automorphism. More precisely, $(X,\rack) $ is a rack provided …