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Homological localization towers for groups and $Π$-modules

About this Title

A. K. Bousfield

Publication: Memoirs of the American Mathematical Society
Publication Year: 1977; Volume 10, Number 186
ISBNs: 978-0-8218-2186-2 (print); 978-1-4704-0052-1 (online)
DOI: https://doi.org/10.1090/memo/0186
MathSciNet review: 0447375

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Table of Contents

Chapters

  • Part I. Homological localization towers for groups
  • 1. Preliminaries on homological localizations of groups
  • 2. HR-closed subgroups and HR-local groups
  • 3. The HR-tower of group and HR-localizations
  • 4. HR-localizations given by $R$-completions
  • 5. Proof of 4.4 and 4.12
  • Part II. Homological localization towers for $\Pi$-modules
  • 6. Preliminaries on homological localizations of $\pi$-modules
  • 7. HZ-closed sub-$\pi$-modules and HZ-local $\pi$-modules
  • 8. The HZ-tower of a $\pi$-module and HZ-localizations
  • 9. The determination of tower modules
  • 10. HZ-localizations given by $I$-adic completions
  • Appendix A. The lower $R$-central series and $R$-completion of a group
  • 11. The lower $R$-central series of a group
  • 12. The $R$-completion of a group
  • 13. An idempotency theorem for $R$-completions
  • 14. An exactness theorem for $R$-completions
  • Appendix B. A comment on homological localizations of spaces
  • 15. Homological localizations with coefficients in $Z/n$