Finite groups in which almost all class sizes are prime numbers

TL;DR

This paper investigates finite groups that have exactly two conjugacy class sizes as composite numbers, exploring their arithmetical and structural properties.

Contribution

It introduces a detailed analysis of finite groups with precisely two composite conjugacy class sizes, a novel focus in group theory.

Findings

Characterization of groups with two composite class sizes

Identification of structural patterns in such groups

Insights into the distribution of class sizes in finite groups

Abstract

In this paper we study arithmetical and structural features of a finite group that possesses exactly two conjugacy class sizes that are composite numbers.