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Camina Triples

Published online by Cambridge University Press:  20 November 2018

Nabil M. Mlaiki
Nabil M. Mlaiki*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA e-mail: nmlaiki2012@gmail.com
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Abstract

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In this paper, we study Camina triples. Camina triples are a generalization of Camina pairs, 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

20D15Camina triplesCamina pairsnilpotent groupsvanishing off subgroupirreducible characterssolvable groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 125 - 131
Copyright
Copyright © Canadian Mathematical Society 2014

References

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