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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
Software:
CHEVIE; GAP
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References:
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