Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T01:50:08.517Z Has data issue: false hasContentIssue false
  • English
  • Français

Partial characters with respect to a normal subgroup

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Gabriel Navarro  and
Lucia Sanus
Gabriel Navarro
Affiliation:
Department d'Algebra, Facultat de Matemátiques, Universitat de Valencia, 46100 Burjassot, Valencia, Spain e-mail: [email protected], [email protected]
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.

Suppose that G is a π-separable group. Let N be a normal π1-subgroup of G and let H be a Hall π-subgroup of G. In this paper, we prove that there is a canonical basis of the complex space of the class functions of G which vanish of G-conjugates ofHN. When N = 1 and π is the complement of a prime p, these bases are the projective indecomposable characters and set of irreduciblt Brauer charcters of G.

Keywords

π-partial charactersBrauer charactersprojective indecomposable charactersπ-separable groups

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 1 , February 1999 , pp. 104 - 124
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Isaacs, I. M., ‘Characters of π-separable groups’, J. Algebra 86 (1984), 98–128.CrossRefGoogle Scholar
[2]Isaacs, I. M., ‘Fong characters in π-separable groups’, J. Algebra 99 (1986), 89–107.CrossRefGoogle Scholar
[3]Isaacs, I. M., ‘Partial characters of π-separable groups’, Prog. Math. 95 (1991), 273–287.Google Scholar
[4]Isaacs, I. M., Character theory of finite groups (Dover, New York, 1994).Google Scholar
[5]Isaacs, I. M., ‘Extensions of characters from Hall π-subgroups of π-separable groups’, Proc. Edinburgh Math. Soc. 38 (1995), 313–317.Google Scholar
[6]Navarro, G., ‘Bases for induced characters’, J. Austral. Math. Soc. (Ser. A) 61 (1996), 369–376.CrossRefGoogle Scholar
[7]Sanus, L., Good bases for induced characters (Ph.D. Thesis, Universitat de Valencia, to appear).Google Scholar