Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T06:37:15.016Z Has data issue: false hasContentIssue false
  • English
  • Français

Unfaithful minimal Heilbronn characters of L2(q)

Part of: Representation theory of groups

Published online by Cambridge University Press:  21 November 2012

Hy Ginsberg
Hy Ginsberg*
Affiliation:
Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, VT 05401, USA
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.

When a minimal Heilbronn character θ is unfaithful on a Sylow p-subgroup P of a finite group G, we know that G is quasi-simple, p is odd, P is cyclic, NG(P) is maximal and either NG(P) is the unique maximal subgroup containing Ω1(P) or G/Z(G) ≅ L2(q) for q an odd prime with p dividing q − 1. In this paper we examine the exceptional case, where G/Z(G) ≅ L2(q), explicitly constructing unfaithful minimal Heilbronn characters from the non-principal irreducible characters of G.

Keywords

Heilbronn charactersvirtual charactersArtin's conjecture

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 57 - 69
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

1.Dornhoff, L., Group representation theory, Part A, Pure and Applied Mathematics, Volume 7 (Marcel Dekker, New York, 1971).Google Scholar
2.Foote, R., Sylow 2-subgroups of Galois groups arising as minimal counterexamples to Artin's conjecture, Commun. Alg. 25(2) (1997), 607–616.CrossRefGoogle Scholar
3.Ginsberg, H., Unfaithful Heilbronn characters of finite groups, J. Alg. 331 (2011), 466–481.CrossRefGoogle Scholar
4.Gorenstein, D., Lyons, R. and Solomon, R., Almost simple K-groups, in The classification of the finite simple groups, Number 3, Mathematical Surveys and Monographs, Volume 40.3, Part I, Chapter A (American Mathematical Society, Providence, RI, 1998).Google Scholar