Galois action on the principal block and generation of Sylow 3-subgroups

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Eden Ketchum, J. Alfredo Martínez, Noelia Rizo, A. A. Schaeffer Fry
DOI: 10.48550/arxiv.2602.14366
Cited by: 0

Abstract

In this paper, we prove one direction of a conjecture of Navarro-Rizo-Schaeffer Fry-Vallejo positing an algorithm to determine from the character table whether a finite group has $2$-generated Sylow $3$-subgroups. This gives further evidence of the blockwise version of the Galois-McKay conjecture (also known as the Alperin-McKay-Navarro conjecture). A key step involves proving the Isaacs-Navarro Galois conjecture for principal blocks for finite groups with a certain structure.

Fields of Study & Subjects

Finite Group Theory Research Advanced Algebra and Geometry Advanced Combinatorial Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
16 February 2026
Language
EN
Document type
Preprint