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Unfaithful minimal Heilbronn characters of L2(q)

Published online by Cambridge University Press:  21 November 2012

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.

Type
Research Article
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), 607616.CrossRefGoogle Scholar
3.Ginsberg, H., Unfaithful Heilbronn characters of finite groups, J. Alg. 331 (2011), 466481.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