  The weights for a finite group G with respect to a prime number p where
introduced by Jon Alperin, in order to formulate his celebrated conjecture
affirming that that the number of G-conjugacy classes of weights of G coincides
with the number of isomorphism classes of simple kG-modules, where k is an
algebraically closed field of characteristic p. Thirty years ago, Tetsuro
Okuyama already proved that in the class of p-solvable groups this conjecture
holds. In this paper, for the p-solvable groups, on the one hand we exhibit a
natural bijection - namely compatible with the action of the group of outer
automorphisms of G - between the sets of isomorphism classes of simple
G-modules M and of G-conjugacy classes of weights (R,Y), up to the choice of a
polarization. On the other hand, we determine the relationship between a
multiplicity module of M and Y. In an Appendix, we show that the bijection
defined by Gabriel Navarro for the groups of odd order coincides with our
bijection for a particular choice of the polarization.
