Characters and generation of Sylow 2-subgroups

We show that the character table of a finite group G determines whether a Sylow 2-subgroup of G is generated by 2 elements, in terms of the Galois action on characters. Our proof of this result requires the use of the Classification of Finite Simple Groups and provides new evidence for the so-far el...

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Bibliographic Details
Published in:Representation theory 2021-02, Vol.25 (5), p.142-165
Main Authors: Navarro, Gabriel, Rizo, Noelia, Schaeffer Fry, A. A., Vallejo, Carolina
Format: Article
Language:English
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Summary:We show that the character table of a finite group G determines whether a Sylow 2-subgroup of G is generated by 2 elements, in terms of the Galois action on characters. Our proof of this result requires the use of the Classification of Finite Simple Groups and provides new evidence for the so-far elusive Alperin-McKay-Navarro conjecture.
ISSN:1088-4165
1088-4165
DOI:10.1090/ert/555