New York Journal of Mathematics
Volume 6 (2000) 55-71


W. A. Bogley and N. D. Gilbert

The Homology of Peiffer Products of Groups

Published: February 15, 2000
Keywords: homology, Peiffer product, asphericity, two-complex, double wreath product
Subject: 20J05, 20E22, 20F05

The Peiffer product of groups first arose in work of J.H.C. Whitehead 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 Peiffer product. We show that a Peiffer product of superperfect groups is superperfect, and determine when a Peiffer product of cyclic groups has trivial second homology. We also introduce a double wreath product as a Peiffer product.


W. A. Bogley would like to thank the Department of Mathematics at Heriot-Watt University, Edinburgh, for its gracious hospitality while this work was in progress. Bogley was supported by a U. K. Engineering and Physical Sciences Research Council Visiting Fellowship (GR/L49932).

Author information

W. A. Bogley:
Department of Mathematics, Kidder 368, Oregon State University, Corvallis, OR 97331-4605, USA

N. D. Gilbert:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland