McKay conjecture

In mathematics, specifically in the field of group theory, the McKay conjecture is a conjecture of equality between the number of irreducible complex characters of degree not divisible by a prime number to that of the normalizer of a Sylow -subgroup. It is named after Canadian mathematician John McKay.

Statement

Suppose is a prime number, is a finite group, and is a Sylow -subgroup. Define

where denotes the set of complex irreducible characters of the group . The McKay conjecture claims the equality

where is the normalizer of in .

References

    • Isaacs, I.M. (1994). Character Theory of Finite Groups. Dover. ISBN 0-486-68014-2. (Corrected reprint of the 1976 original, published by Academic Press.)
    • Evseev, Anton (2013). "The McKay Conjecture and Brauer's Induction Theorem". Proceedings of the London Mathematical Society. 106: 1248–1290. arXiv:1009.1413. doi:10.1112/plms/pds058.
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