Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T14:52:41.410Z Has data issue: false hasContentIssue false
  • English
  • Français

The nuclear length of a character

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Wayne W. Wheeler
Wayne W. Wheeler
Affiliation:
School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, (e-mail: [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.

If G is a π-separable group and χ is an irreducible character of G, then Issacs gas defined an associated pair (W, γ), called a nucleus of χ. The nucleus is the last term in a certain chain of pairs (I, Ω), where I is a subgroup of G and Ω is an irreducible character of I. The length of this chain is an invariant of χ that we call the nuclear length. In this paper we study bounds on the nuclear length of χ as a function of the π-length of G and as a function of the character degree χ(1).

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 49 - 59
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Gajendragadkar, D., ‘A characteristic class of characters of finite π-separable groups’, J. Algebra 59 (1979), 237–259.Google Scholar
[2]Isaacs, I. M., ‘Characters of π-separable groups’, J. Algebra 86 (1984), 98–128.CrossRefGoogle Scholar
[3]Isaacs, I. M. and Navarro, G., ‘Weights and vertices for characters of π-separable groups’, preprint.Google Scholar
[4]Slattery, M., ‘Pi-blocks of pi-separable groups, I’, J. Algebra 102 (1986), 60–77.Google Scholar
[5]Slattery, M., ‘Pi-blocks of pi-separable groups, II’, J. Algebra 124 (1989), 236–269.CrossRefGoogle Scholar
[6]Slattery, M., ‘Pi-blocks of pi-separable groups, III’, J. Algebra 158 (1993), 268–278.CrossRefGoogle Scholar