Vol. 14, No. 7, 2020

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Galois action on the principal block and cyclic Sylow subgroups

Noelia Rizo, A. A. Schaeffer Fry and Carolina Vallejo

Vol. 14 (2020), No. 7, 1953–1979
DOI: 10.2140/ant.2020.14.1953
Abstract

We characterize finite groups G having a cyclic Sylow p-subgroup in terms of the action of a specific Galois automorphism on the principal p-block of G, for p = 2,3. We show that the analog statement for blocks with arbitrary defect group would follow from the blockwise McKay–Navarro conjecture.

Keywords
principal $p$-block, Galois action on characters, cyclic Sylow $p$-subgroups, Alperin–McKay–Navarro Conjecture
Mathematical Subject Classification 2010
Primary: 20C15
Secondary: 20C20, 20C33
Milestones
Received: 11 December 2019
Revised: 10 February 2020
Accepted: 10 March 2020
Published: 18 August 2020
Authors
Noelia Rizo
Università degli Studi di Firenze
Italy
A. A. Schaeffer Fry
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver
CO
United States
Carolina Vallejo
Departamento de Matemáticas
Universidad Autónoma de Madrid
Facultad de Ciencias
Campus de Cantoblanco
Madrid
Spain