The Dade group of Mackey functors for p-groups

Abstract

We introduce endo-permutation Mackey functors and the Mackey-Dade group of a p-group and study their basic properties. We exhibit relations between the Mackey-Dade group of a finite p-group P and the Dade groups of the Weyl groups of all subgroups of P . As a result, we show that the Mackey-Dade group tensored with Q over Z is the kernel of the linearization map for Mackey functors, introduced by the author.