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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
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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 Camina triples, Camina pairs, nilpotent groups, vanishing off subgroup, irreducible characters, solvable groups
MSC Classifications: 20D15 show english descriptions Nilpotent groups, $p$-groups 20D15 - Nilpotent groups, $p$-groups
 

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