The homology of Peiffer products of groups

W. A. Bogley, N. D. Gilbert

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The Peiffer product of groups first 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 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.

Original languageEnglish
Pages (from-to)55-71
Number of pages17
JournalNew York Journal of Mathematics
Volume6
Publication statusPublished - 2000

Keywords

  • Asphericity
  • Double wreath product
  • Homology
  • Peiffer product
  • Two-complex

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