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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
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 $Z/n$