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RESEARCH PRODUCT

p-Length andp′-Degree Irreducible Characters Having Values in ℚp

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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 ℚ 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 ℚ p .