Journal of Lie Theory

no. 1
On Self-Normalising Sylow 2-Subgroups in Type A
Amanda A. Schaeffer Fry1; Jay Taylor2
1Dept. of Mathematics, MSU Denver, Campus Box 38, Denver, CO 80217-3362, U.S.A.
2Dept. of Mathematics, University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ 85721, U.S.A.
Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 139-168
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.
DOI: 10.5802/jolt.997
Classification: 20C15, 20C33
Keywords: Finite groups, Galois-McKay conjecture, Sylow 2-subgroups

Amanda A. Schaeffer Fry  1 ; Jay Taylor  2

1 Dept. of Mathematics, MSU Denver, Campus Box 38, Denver, CO 80217-3362, U.S.A.
2 Dept. of Mathematics, University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ 85721, U.S.A. 
Amanda A. Schaeffer Fry; Jay Taylor. On Self-Normalising Sylow 2-Subgroups in Type A. Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 139-168. doi: 10.5802/jolt.997
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