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.

12 pages

References in corpus (1)

• Inductive McKay Condition in defining Characteristic