A partition of characters associated to nilpotent subgroups

If G is a finite solvable group and H is a maximal nilpotent subgroup of G containing F(G), we show that there is a canonical basis P(G\H) of the spac e of class functions on G vanishing off any G-conjugate of H which consists of characters. Via P(G\H) it is possible to partition the irreducible char acters of G into "blocks". These behave like Brauer p-blocks and a Fong the ory for them can be developed.