A lower bound for the number of conjugacy classes of a finite group

TL;DR

This paper establishes a lower bound on the number of conjugacy classes in finite groups based on their order and prime divisors, contributing to the understanding of group structure.

Contribution

It provides a new lower bound for the number of conjugacy classes in finite groups divisible by a prime p, advancing theoretical knowledge.

Findings

Finite groups divisible by prime p have at least 2√(p-1) conjugacy classes.

The bound improves understanding of the relationship between group order and conjugacy class count.

Abstract

Every finite group whose order is divisible by a prime $p$ has at least $2 \sqrt{p-1}$ conjugacy classes.