Class Group Relations from Burnside Ring Idempotents

Abstract

We show that for each finite cohomological Mackey functor on a finite groupGthere exist explicit relations in the category of finite abelian groups between the evaluations of the Mackey functor at all the subgroups, one for each conjugacy class of nonhypo-elementary subgroups ofG. Furthermore, we show that the class groups of the intermediate fields of a Galois extension of number fields form such a Mackey functor on the Galois group, thereby obtaining class group relations by using the presence of the structure of a cohomological Mackey functor. © 1997 Academic Press.