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FINITE GROUPS WITH TWO p-REGULAR CONJUGACY CLASS LENGTHS II

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  17 April 2009

ELENA ALEMANY ,
ANTONIO BELTRÁN  and
MARÍA JOSÉ FELIPE
ELENA ALEMANY
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain (email: ealemany@mat.upv.es)
ANTONIO BELTRÁN*
Affiliation:
Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain (email: abeltran@mat.uji.es)
MARÍA JOSÉ FELIPE
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain (email: mfelipe@mat.upv.es)
*
✉For correspondence; e-mail: abeltran@mat.uji.es
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Abstract

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Let G be a finite group. We prove that if the set of p-regular conjugacy class sizes of G has exactly two elements, then G has Abelian p-complement or G=PQ×A, with P∈Sylp(G), Q∈Sylq(G) and A Abelian.

Keywords

finite-groupsp-regular elementsconjugacy class sizes

MSC classification

Secondary: 20E45: Conjugacy classes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 419 - 425
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work was partially supported by grant MTM2007-68010-C03-03 and the second author is also supported by grant Fundació Caixa-Castelló P1-1A2006-06.

References

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