Abstract
Let N < G where G is a finite group and let B be a p-block of G, where p is a prime. A Brauer character ψ ∈ IBr_p(B) is said to be of relative height zero with respect to N provided that the height of ψ is equal to that of an irreducible constituent of ψ_N . Now assume G is p-solvable. In this paper, we count the number of relative height zero irreducible Brauer characters of B with respect to N that lie over any given ψ ∈ IBr_p(N). As a consequence, we show that if D is a defect group of B and B is the unique p-block of N N_G(D) with defect group D such that B^G = B, then B and B have equal numbers of relative height zero irreducible Brauer characters with respect to N.