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.
Characters and Generation of Sylow 2-Subgroups / Navarro G.; Rizo N.; schaeffer Fry A.A.; Vallejo C.. - In: REPRESENTATION THEORY. - ISSN 1088-4165. - ELETTRONICO. - 25:(2021), pp. 142-165. [10.1090/ert/555]
Characters and Generation of Sylow 2-Subgroups
Vallejo C.
2021
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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