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Characters and generation of Sylow 2-subgroups. (English) Zbl 07325593
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.
##### MSC:
 20C20 Modular representations and characters 20C15 Ordinary representations and characters
CHEVIE; GAP
Full Text:
##### References:
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