Camina triples

In this paper, we study Camina triples. Camina triples are a generalization of Camina pairs. Camina pairs were first introduced in 1978 by A.R. Camina in \cite{camina1}. Camina’s work in \cite{camina1} was inspired by the study of Frobenius groups. We show that if $(G,N,M)$ is a Camina triple, then either $G\mathrm{/}N$ is a $p$-group, $M$ is nilpotent, or $M$ has a non-trivial nilpotent quotient.