The Isaacs-Navarro Conjecture for covering groups of the symmetric and alternating groups in odd characteristic

TL;DR

This paper proves a refined version of the Alperin-McKay Conjecture for covering groups of symmetric and alternating groups in odd characteristic, confirming its validity in this specific context.

Contribution

It establishes the Isaacs-Navarro Conjecture for covering groups of symmetric and alternating groups in odd characteristic, extending the scope of the conjecture to these complex groups.

Findings

Refinement of the Alperin-McKay Conjecture holds for these groups

Validates the conjecture for all covering groups of symmetric and alternating groups in odd characteristic

Advances understanding of block theory in finite groups

Abstract

In this paper, we prove that a refinement of the Alperin-McKay Conjecture for $p$-blocks of finite groups, formulated by I. M. Isaacs and G. Navarro in 2002, holds for all covering groups of the symmetric and alternating groups, whenever $p$ is an odd prime.