The Homology of Peiier Products of Groups

The Peiier product of groups rst arose in work of J.H.C. White-head on the structure of relative homotopy groups, and is closely related to problems of asphericity for two-complexes. We develop algebraic methods for computing the second integral homology of a Peiier product. We s h o w t h a t a Peiier product of superperfect groups is superperfect, and determine when a Peiier product of cyclic groups has trivial second homology. W e also introduce a double wreath product as a Peiier product.