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

The Homology of Peiffer Products of Groups

W. A. Bogley and N. D. Gilbert

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

Abstract:

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.

Acknowledgments:
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
bogley@math.orst.edu
http://ucs.orst.edu/~bogleyw/

N. D. Gilbert:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
N.D.Gilbert@ma.hw.ac.uk
http://www.ma.hw.ac.uk/~nick/