Cancellation theorems related to conjectures of Alperin and Dade (Q1614634)

Previously, the author and \textit{R.~Staszewski} [Astérisque 181-182, 237-255 (1990; Zbl 0703.20008)] showed that the Knörr-Robinson formulation of Alperin's weight conjecture is compatible with Clifford-theoretic reductions. These led to simplifications in some alternating sum calculations. Here the author gives analogous results for Dade's projective conjecture, which result in a new proof of this conjecture in the \(p\)-solvable case, with some refinements as well.