Brauer character degrees and Sylow normalizers
The main result proved by the authors is Theorem A, which may be expressed as follows: Let \(p\) and \(q\) be (not necessarily distinct) primes, and let \(G\) be a finite \(p\)-solvable group. Then the (mod \(p\)) irreducible Brauer characters of degree prime to \(q\) all have degree prime to \(p\) if and only if some Sylow \(p\)-subgroup of \(G\) is normalized by the normalizer of a Sylow \(q\)-subgroup of \(G\). The proof of this result makes use of the classification of the finite simple groups.
scientific article; zbMATH DE number 7605302
scientific article