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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

[1] Camina, A. R., Some Conditions Which Almost Characterize Frobenius Groups. Israel J. Math. 31 (1978), 153–160. http://dx.doi.org/10.1007/BF02760546 Google Scholar
[2] Chillag, D. and MacDonald, I. D., Generalized Frobenius Groups. Israel J. Math. 47 (1984), 111–122. http://dx.doi.org/10.1007/BF02760510 Google Scholar
[3] Dark, R. and Scoppola, C. M., On Camina Groups of Prime Power Order. J. Algebra 181 (1996), 787–802 http://dx.doi.org/10.1006/jabr.1996.0146 Google Scholar
[4] Isaacs, I. M., Character Theory of Finite Groups. Academic Press, San Diego, California, 1976.Google Scholar
[5] Isaacs, I. M., Algebra A Graduate Course. Academic Press, Pacific Grove, California, 1993.Google Scholar
[6] Isaacs, I. M., Finite Group Theory. Amer. Math. Soc., Providence, Rhode Island, 2008.Google Scholar
[7] Isaacs, I. M. and Greg Knutson, Irreducible Character Degrees and Normal subgroups. J. Algebra 199 (1998), 302–326. http://dx.doi.org/10.1006/jabr.1997.7191 Google Scholar
[8] Lewis, M. L., The vanishing-off subgroup. J. Algebra 321 (2009), 1313–1325. http://dx.doi.org/10.1016/j.jalgebra.2008.11.024 Google Scholar
[9] MacDonald, I. D., Some p-Groups of Frobenius And Extra-Special Type. Israel J. Math. 40 (1981), 350–364. http://dx.doi.org/10.1007/BF02761376 Google Scholar
[10] MacDonald, I. D., More on p-Groups of Frobenius Type. Israel J. Math. 56 (1986), 335–344. http://dx.doi.org/10.1007/BF02782940 Google Scholar