On p′-degree ℓ-Brauer characters of ℓ-solvable groups

Abstract

Let [Formula: see text] and [Formula: see text] be distinct primes, let [Formula: see text] be a finite [Formula: see text]-solvable group and let [Formula: see text]. Then [Formula: see text] has a unique irreducible [Formula: see text]-Brauer character of [Formula: see text]-degree lying over [Formula: see text] if and only if NG (P)/ P is an [Formula: see text]-group. This extends a result from [J., F.,Tent, Correspondences of Brauer characters and Sylow subgroup normalizers, J. Algebra 573 (2021) 436–450] to every odd prime [Formula: see text].