The Projective Height Zero Conjecture

TL;DR

This paper introduces a projective variant of Brauer's Height Zero Conjecture, proves it for specific classes of finite groups, and advances understanding of character theory in group representations.

Contribution

It formulates and proves a projective version of Brauer's Height Zero Conjecture for p-solvable and certain quasi-simple groups, extending classical results.

Findings

Proved the conjecture for p-solvable groups

Established the conjecture for some quasi-simple groups

Extended the scope of the classical Brauer's conjecture

Abstract

We propose a projective version of the celebrated Brauer's Height Zero Conjecture on characters of finite groups and prove it, among other cases, for $p$-solvable groups as well as for (some) quasi-simple groups.