Finite groups have even more conjugacy classes

TL;DR

This paper improves the known lower bounds on the number of conjugacy classes in finite groups, strengthening previous results by Pyber, and thus advances understanding of group structure.

Contribution

It provides stronger lower bounds for the number of conjugacy classes in finite groups compared to prior work by Pyber.

Findings

Established new lower bounds for conjugacy classes

Enhanced theoretical understanding of finite group structure

Strengthened previous mathematical results

Abstract

In his paper "Finite groups have many conjugacy classes" (J. London Math. Soc (2) 46 (1992), 239-249), L. Pyber proved the to date best general lower bounds for the number of conjugacy classes of a finite group in terms of the order of the group. In this paper we strengthen the main results in Pyber's paper.