The Homology of Peiffer Products of Groups

摘要

The Peiffer product of groups first arose in workof J.H.C. Whitehead on the structure of relative homotopy groups, and isclosely related to problems of asphericity for two-complexes. We developalgebraic methods for computing the second integral homology of a Peifferproduct. We show that a Peiffer product of superperfect groups issuperperfect, and determine when a Peiffer product of cyclic groups hastrivial second homology. We also introduce a double wreath product as aPeiffer product.