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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
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Abstract

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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

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