Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T13:26:28.614Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

1. Broshi, A. M., Galois correspondences between the irreducible characters and the conjugacy classes of finite groups, J. Alg. 19 (1971), 441–451.CrossRefGoogle Scholar
2. Dade, E. C., Galois actions on characters and on classes, preprint.Google Scholar
3. Graves, J. S., Glauberman-Isaacs correspondence and π-Brauer characters, J. Alg. 169 (1994), 891–901.CrossRefGoogle Scholar
4. Isaacs, M., Characters of π-separable groups, J. Alg. 86 (1984), 98–128.CrossRefGoogle Scholar
5. Isaacs, M., Character theory of finite groups, Number 359 (AMS Chelsea, Providence, RI, 2006).Google Scholar
6. Isaacs, M., Navarro, G. and Sanus, L., Field of values of Fong characters, Arch. Math. 86 (2006), 305–309.CrossRefGoogle Scholar
7. Navarro, G., Fields, values and character extensions in finite groups, J. Group Theory 10 (2007), 279–285.CrossRefGoogle Scholar
8. Navarro, G., Quadratic characters in groups of odd order, J. Alg. 322 (2009), 2586–2589.CrossRefGoogle Scholar
9. Navarro, G. and Tiep, P. H., Rational irreducible characters and rational conjugacy classes in finite groups, Trans. Am. Math. Soc. 360 (2008), 2443–2465.CrossRefGoogle Scholar
10. Wilde, T., The real part of the character table of a finite group, Commun. Alg. 35 (2007), 4042–4056.CrossRefGoogle Scholar
11. Wolf, T. R., Character correspondences and π-special characters in π-separable groups. Can. J. Math. 39 (1987), 920–937.CrossRefGoogle Scholar