On the projective height zero conjecture

TL;DR

This paper demonstrates that Brauer's original height zero conjecture implies a recently proposed projective version, establishing a logical connection between the two conjectures in the context of finite group blocks.

Contribution

It proves that Brauer's height zero conjecture implies the projective height zero conjecture, linking the two conjectures and advancing understanding in the representation theory of finite groups.

Findings

Brauer's conjecture implies the projective version

Establishes a logical implication between the two conjectures

Contributes to the theoretical understanding of block theory

Abstract

Recently, Malle and Navarro put forward a projective version of Brauer's celebrated height zero conjecture on blocks of finite groups. In this short note we show that Brauer's original conjecture implies the projective version.