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Finite p-solvable groups with three p-regular conjugacy class sizes

Published online by Cambridge University Press:  30 August 2012

Zeinab Akhlaghi
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran (z_akhlaghi@aut.ac.ir; m_khatami@aut.ac.ir)
Antonio Beltrán
Affiliation:
Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain (abeltran@mat.uji.es)
María José Felipe
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain (mfelipe@mat.upv.es)
Maryam Khatami
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran (z_akhlaghi@aut.ac.ir; m_khatami@aut.ac.ir)
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Abstract

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Let G be a finite p-solvable group. We describe the structure of the p-complements of G when the set of p-regular conjugacy classes has exactly three class sizes. For instance, when the set of p-regular class sizes of G is {1, pa, pam} or {1, m, pam} with (m, p) = 1, then we show that m = qb for some prime q and the structure of the p-complements of G is determined.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2013

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