Galois automorphisms on Harish-Chandra series and Navarro's self-normalizing Sylow 2-subgroup conjecture

Navarro has conjectured a necessary and sufficient condition for a finite group G to have a self-normalizing Sylow 2-subgroup, which is given in terms of the ordinary irreducible characters of G. In a previous article, Schaeffer Fry has reduced the proof of this conjecture to showing that certain re...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-07, Vol.372 (1), p.457-483
Main Author: FRY, A. A. SCHAEFFER
Format: Article
Language:English
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Summary:Navarro has conjectured a necessary and sufficient condition for a finite group G to have a self-normalizing Sylow 2-subgroup, which is given in terms of the ordinary irreducible characters of G. In a previous article, Schaeffer Fry has reduced the proof of this conjecture to showing that certain related statements hold for simple groups. In this article, we describe the action of Galois automorphisms on the Howlett-Lehrer parametrization of Harish-Chandra induced characters. We use this to complete the proof of the conjecture by showing that the remaining simple groups satisfy the required conditions.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7590