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Rationality and Sylow 2-subgroups

Part of: Representation theory of groups

Published online by Cambridge University Press:  12 August 2010

Gabriel Navarro  and
Joan Tent
Gabriel Navarro
Affiliation:
Departament d'Àlgebra, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain (gabriel.navarro@uv.es; joan.tent@uv.es)
Joan Tent
Affiliation:
Departament d'Àlgebra, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain (gabriel.navarro@uv.es; joan.tent@uv.es)
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Abstract

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Let G be a finite group. If G has a cyclic Sylow 2-subgroup, then G has the same number of irreducible rational-valued characters as of rational conjugacy classes. These numbers need not be the same even if G has Klein Sylow 2-subgroups and a normal 2-complement.

Keywords

rational charactersrational classescharacters

MSC classification

Secondary: 20C15: Ordinary representations and characters 20C20: Modular representations and characters
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 787 - 798
Copyright
Copyright © Edinburgh Mathematical Society 2010

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