Brauer's height zero conjecture for quasi-simple goups

TL;DR

This paper proves Brauer's height zero conjecture for blocks of finite quasi-simple groups, advancing the understanding of modular representation theory and supporting broader conjectures in the field.

Contribution

It establishes the conjecture for quasi-simple groups, enabling reduction of the problem to simple groups via existing frameworks.

Findings

Brauer's height zero conjecture verified for quasi-simple groups

Supports reduction of conjecture to simple groups

Facilitates progress on the Alperin-McKay conjecture

Abstract

We show that Brauer's height zero conjecture holds for blocks of finite quasi-simple groups. This result is used in Navarro-Sp\"ath's reduction of this conjecture for general groups to the inductive Alperin-McKay condition for simple groups.