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RESEARCH PRODUCT

Sylow subgroups, exponents, and character values

subject

description

If G G is a finite group, p p is a prime, and P P is a Sylow p p -subgroup of G G , we study how the exponent of the abelian group P / P ′ P/P’ is affected and how it affects the values of the complex characters of G G . This is related to Brauer’s Problem 12 12 . Exactly how this is done is one of the last unsolved consequences of the McKay–Galois conjecture.