The Class Number of Derived Subgroups and the Structure of Camina Groups

Abstract

A finite group $G$ is called a Camina group if $G$ has a proper normal subgroup $N$ such that $gN$ is precisely a conjugacy class of $G$ for any $g ∈ G − N$. In this paper, the structure of a Camina group $G$ is determined when $N$ is a union of 2, 3 or 4 conjugacy classes of $G$.