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

Thomas Michael Keller

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

Group Theory 2007-08-20 v1

Authors: Thomas Michael Keller

Abstract

In 2000, L. H\'{e}thelyi and B. K\"{u}lshammer 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.

Keywords

conjugacy classes finite groups lower bound solvable groups prime number group order

Cite

@article{arxiv.0708.2281,
  title  = {A lower bound for the number of conjugacy classes of finite groups},
  author = {Thomas Michael Keller},
  journal= {arXiv preprint arXiv:0708.2281},
  year   = {2007}
}

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