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Unfaithful minimal Heilbronn characters of L2(q)

  • Hy Ginsberg (a1)

Abstract

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.

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1.Dornhoff, L., Group representation theory, Part A, Pure and Applied Mathematics, Volume 7 (Marcel Dekker, New York, 1971).
2.Foote, R., Sylow 2-subgroups of Galois groups arising as minimal counterexamples to Artin's conjecture, Commun. Alg. 25(2) (1997), 607616.
3.Ginsberg, H., Unfaithful Heilbronn characters of finite groups, J. Alg. 331 (2011), 466481.
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).

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Unfaithful minimal Heilbronn characters of L2(q)

  • Hy Ginsberg (a1)

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