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Journal of Lie Theory 28 (2018), No. 1, 139--168
Copyright Heldermann Verlag 2018

On Self-Normalising Sylow 2-Subgroups in Type A

Amanda A. Schaeffer Fry
Dept. of Mathematics, MSU Denver, Campus Box 38, Denver, CO 80217-3362, U.S.A.

Jay Taylor
Dept. of Mathematics, University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ 85721, U.S.A.

Navarro has conjectured a necessary and sufficient condition for a finite group G to have a self-normalising Sylow 2-subgroup, which is given in terms of the ordinary irreducible characters of G. The first-named author has reduced the proof of this conjecture to showing that certain related statements hold when G is quasisimple. In this article we show that these conditions are satisfied when G/Z(G) is PSLn(q), PSUn(q), or a simple group of Lie type defined over a finite field of characteristic 2.

Keywords: Finite groups, Galois-McKay conjecture, Sylow 2-subgroups.

MSC: 20C15, 20C33

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