A Frobenius group analog for Camina triples

Abstract

Frobenius groups are an object of fundamental importance in finite group theory. As such, several generalizations of these groups have been considered. Some examples include: A Frobenius--Wielandt group is a triple $(G,H,L)$ where $H/L$ is {\it almost} a Frobenius complement for $G$; A Camina pair is a pair $(G,N)$ where $N$ is {\it almost} a Frobenius kernel for $G$; A Camina triple is a triple $(G,N,M)$ where $(G,N)$ and $(G,M)$ are {\it almost} Camina pairs. In this paper we study triples $(G,N,M)$ where $(G,N)$ and $(G,M)$ are {\it almost} Frobenius groups.