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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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Additional Information

Gabriel Navarro
Affiliation: Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
MR Author ID: 129760
Email: gabriel@uv.es

Noelia Rizo
Affiliation: Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
MR Author ID: 1070925
Email: noelia.rizo@uv.es

A. A. Schaeffer Fry
Affiliation: Department of Mathematics and Statistics, MSU Denver, Denver, Colorado 80217
MR Author ID: 899206
Email: aschaef6@msudenver.edu

Carolina Vallejo
Affiliation: Departamento de Matemáticas, Edificio Sabatini, Universidad Carlos III de Madrid, Av. Universidad 30, 28911, Leganés. Madrid, Spain
MR Author ID: 1001337
ORCID: 0000-0003-3363-3376
Email: carolina.vallejo@uc3m.es

Keywords: Sylow 2-subgroups, character tables, principal blocks, Alperin–Galois–McKay conjecture
Received by editor(s): March 18, 2020
Received by editor(s) in revised form: April 1, 2020
Published electronically: February 25, 2021
Additional Notes: The first, second and fourth authors were partially supported by the Spanish Ministerio de Ciencia e Innovación PID2019-103854GB-I00 and FEDER funds. The third author was partially supported by the National Science Foundation under Grant No. DMS-1801156. The fourth author also acknowledges support by Spanish Ministerio de Ciencia e Innovación MTM2017-82690-P and the ICMAT Severo Ochoa project SEV-2015-0554. Part of this work was supported by the National Security Agency under Grant No. H98230-19-1-0119, The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research, while the second, third, and fourth authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2019.
Article copyright: © Copyright 2021 American Mathematical Society