McKay Conjecture

The McKay Conjecture is a hypothesis in the field of finite group theory, suggesting a deep relationship between the symmetry properties of a group and its prime factors. Specifically, it proposes that, for any prime number p, the number of irreducible representations (building blocks of symmetries) of a finite group related to p equals the number of such representations in a special subgroup called the normalizer of a Sylow p-subgroup. This conjecture aims to connect local subgroup structure with the overall symmetry properties of the entire group, potentially simplifying the classification of complex algebraic structures.