The McKay Conjecture and central isomorphic character triples

TL;DR

This paper refines the reduction theorem for the McKay Conjecture, establishing a stronger version that involves central isomorphic character triples under the inductive condition.

Contribution

It introduces a refined reduction theorem for the McKay Conjecture, linking it to central isomorphic character triples assuming the inductive condition.

Findings

Refined the reduction theorem for the McKay Conjecture.

Established a strong version involving central isomorphic character triples.

Connected the conjecture's validity to the inductive McKay condition.

Abstract

We refine the reduction theorem of the McKay Conjecture proved by Isaacs, Malle and Navarro. Assuming the inductive McKay condition, we obtain a strong version of the McKay Conjecture that gives central isomorphic character triples.