Pseudocompact algebras, profinite groups and class formations

Introduction. We recall that a topological group G is a profinite group if it is the inverse limit of finite groups and that a G-module A is a discrete G-module if A — \)AH, where H runs through the open subgroups of G and AH is the set of elements of A left fixed by H (cf. [4]). We note tha t if H is a normal subgroup of Ky then A H is a K/H-module. A class formation consists of a profinite group G and a G-module satisfying certain axioms which we do not repeat here: the reader will find them and their consequences in [ l ] . The reciprocity map for the formation gives a homomorphism