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.
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 (Corrected reprint of the 1976 original, published by Academic Press. ed.). Dover. ISBN 0-486-68014-2.
- Evseev, Anton (2011). "The McKay Conjecture and Brauer's Induction Theorem". Proceedings of the London Mathematical Society. 106: 1248–1290. arXiv:1009.1413 [math.RT]. doi:10.1112/plms/pds058. Cite uses deprecated parameter
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