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arXiv · 2602.14366

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

Eden Ketchum·J. Miquel Martínez·Noelia Rizo·A. A. Schaeffer Fry
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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.

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Eden Ketchum, J. Miquel Martínez, Noelia Rizo, A. A. Schaeffer Fry. 2026-02-16. Galois action on the principal block and generation of Sylow 3-subgroups. https://arxiv.org/abs/2602.14366

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