Character heights and p-length in blocks of p-solvable groups

We give the lower bounds 2ℓ and 2ℓ−2+2ℓ−4+⋯ for the number of irreducible characters of height zero and positive height, respectively, in a p-block of a p-solvable group, where ℓ is the p-length of an associated p-solvable group. We also prove some results on extensions of linear characters in p-subgroups of p-solvable groups.