A lower bound for the number of conjugacy classes of finite groups

Abstract

In 2000, L. Héthelyi and B. Külshammer proved that if $p$ is a prime number dividing the order of a finite solvable group $G$, then $G$ has at least $2\sqrt{p-1}$ conjugacy classes. In this paper we show that if $p$ is large, the result remains true for arbitrary finite groups.