p-Length and p′-Degree Irreducible Characters Having Values in □_p

摘要

Let G be a p-solvable group of p-length l, where p is any prime. We show that G has at least 2~l irreducible characters of degree coprime to p and having values inside □_p. This generalizes a previous result for p = 2 [6] to arbitrary primes. With the same notation, we prove that if p is odd then G has at least 2~l Galois orbits of conjugacy classes of p-elements having values in □_p.