Characters and generation of Sylow 2-subgroups

Navarro, Gabriel; Rizo, Noelia; Schaeffer Fry, A.; Vallejo, Carolina

doi:10.1090/ert/555

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Characters and generation of Sylow 2-subgroups

Authors: Gabriel Navarro, Noelia Rizo, A. A. Schaeffer Fry and Carolina Vallejo
Journal: Represent. Theory 25 (2021), 142-165
MSC (2020): Primary 20C20, 20C15
DOI: https://doi.org/10.1090/ert/555
Published electronically: February 25, 2021
MathSciNet review: 4220651
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Abstract: 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.

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