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Certain relations between p-regular class sizes and the p-structure of p-solvable groups

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

Published online by Cambridge University Press:  09 April 2009

Antonio Beltrán  and
María José Felipe
Antonio Beltrán
Affiliation:
Department o de Matemáticas, Universidad Jaume I, Castellón 12071, Spain e-mail: abeltran@mat.uji.es
María José Felipe
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Valencia 46022, Spain e-mail: mfelipe@mat.upv.es
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Abstract

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Let G be a finite p-solvable group for a fixed prime p. We study how certain arithmetical conditions on the set of p-regular conjugacy class sizes of G influence the p-structure of G. In particular, the structure of the p-complements of G is described when this set is {1, m, n} for arbitrary coprime integers m, n > 1. The structure of G is determined when the noncentral p-regular class lengths are consecutive numbers and when all of them are prime powers.

MSC classification

Secondary: 20E45: Conjugacy classes 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 387 - 400
Copyright
Copyright © Australian Mathematical Society 2004

References

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