Principal $2$-Blocks and Sylow $2$-Subgroups

Abstract

Let $G$ be a finite group with Sylow $2$-subgroup $P⩽G$. Navarro-Tiep-Vallejo have conjectured that the principal $2$-block of $N_G(P)$ contains exactly one irreducible Brauer character if and only if all odd-degree ordinary irreducible characters in the principal $2$-block of $G$ are fixed by a certain Galois automorphism $\sigma \in \mathrm{Gal}({\mathbb{Q}}_{|G|}/\mathbb{Q})$. Recent work of Navarro-Vallejo has reduced this conjecture to a problem about finite simple groups. We show that their conjecture holds for all finite simple groups, thus establishing the conjecture for all finite groups.

arXiv comment12 pages

References in corpus (1)

• Inductive McKay Condition in defining Characteristic