A Divisibility Problem in the McKay Conjecture

TL;DR

This paper explores a variation of the McKay Conjecture in representation theory using GAP software and Kuhn's Algorithm to computationally test the conjecture across finite groups.

Contribution

It introduces a computational approach to investigate a divisibility variation of the McKay Conjecture using GAP and Kuhn's Algorithm.

Findings

Successful computational testing of the conjecture on various groups

Identification of cases supporting the conjecture

Potential counterexamples or limitations discovered

Abstract

The mathematical software \texttt{GAP} (Groups, Algorithms, Programming) offers a powerful set of tools to investigate computationally group theory. Using this software package we investigate a variation of a well-known problem in representation theory, the McKay Conjecture, that asserts that there is a bijection between two sets of complex-valued functions defined on two finite groups. In order to do so, we use the extensive group database from \texttt{GAP} and Kuhn's Algorithm in order to test our conjecture.