Nilpotency of normal subgroups having two class sizes
Authors:
Elena Alemany, Antonio Beltrán and María José Felipe
Journal:
Proc. Amer. Math. Soc. 139 (2011), 26632669
MSC (2010):
Primary 20E45, 20D15
Published electronically:
December 22, 2010
MathSciNet review:
2801605
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Additional Information
Abstract: Let be a finite group. If is a normal subgroup which has exactly two conjugacy class sizes, then is nilpotent. In particular, we show that is abelian or is the product of a group by a central subgroup of . Furthermore, when is not abelian, has exponent .
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Additional Information
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
DOI:
http://dx.doi.org/10.1090/S000299392010107025
Received by editor(s):
June 3, 2010
Received by editor(s) in revised form:
July 14, 2010
Published electronically:
December 22, 2010
Additional Notes:
This work is part of the first author’s Ph.D. thesis and is partially supported by Proyecto MTM200768010C0303 and by Proyecto GV2009021
The second author is also supported by grant Fundació CaixaCastelló P11B200809.
Communicated by:
Jonathan I. Hall
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
