Class Group Relations from Burnside Ring Idempotents

Robert Boltje
University of California, Santa Cruz
http://math.uscs.edu/~boltje

Abstract:
We show that for each finite cohomological Mackey functor on a
finite group $G$ there 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
non-hypo-elementary subgroups of $G$. 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.

Published in:
J. Number Theory 66 (1997), 291-305.