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

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  30 August 2012

Zeinab Akhlaghi ,
Antonio Beltrán ,
María José Felipe  and
Maryam Khatami
Zeinab Akhlaghi
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran ([email protected]; [email protected])
Antonio Beltrán
Affiliation:
Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain ([email protected])
María José Felipe
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain ([email protected])
Maryam Khatami
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran ([email protected]; [email protected])
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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.

Keywords

finite p-solvable groupsconjugacy class sizesp-regular elements

MSC classification

Secondary: 20E45: Conjugacy classes 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 2 , June 2013 , pp. 371 - 386
Copyright
Copyright © Edinburgh Mathematical Society 2013

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