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# Camina Triples

Published:2013-06-14
Printed: Mar 2014
• Nabil M. Mlaiki,
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA
 Format: LaTeX MathJax PDF

## Abstract

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. Camina's work was inspired by the study of Frobenius groups. We show that if $(G,N,M)$ is a Camina triple, then either $G/N$ is a $p$-group, or $M$ is abelian, or $M$ has a non-trivial nilpotent or Frobenius quotient.
 Keywords: Camina triples, Camina pairs, nilpotent groups, vanishing off subgroup, irreducible characters, solvable groups
 MSC Classifications: 20D15 - Nilpotent groups, $p$-groups