6533b7dcfe1ef96bd12728da

RESEARCH PRODUCT

Correspondences of Brauer characters and Sylow subgroup normalizers

Joan Tent

subject

Algebra and Number TheoryDegree (graph theory)Group (mathematics)010102 general mathematicsSylow theorems01 natural sciencesCombinatoricsCharacter (mathematics)0103 physical sciencesBijection010307 mathematical physics0101 mathematicsMathematics::Representation TheoryMathematics

description

Abstract Let p > 3 and q ≠ p be primes, let G be a finite q-solvable group and let P ∈ Syl p ( G ) . Then G has a unique irreducible q-Brauer character of p ′ -degree lying over 1 P if and only if N G ( P ) / P is a q-group. One direction of this result follows from a natural McKay bijection of p ′ -degree irreducible q-Brauer characters, which is obtained under suitable conditions.

https://doi.org/10.1016/j.jalgebra.2021.01.003