Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-08T20:01:22.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Localization methods in the study of the homology of virtually nilpotent groups

Published online by Cambridge University Press:  24 October 2008

Carles Casacuberta  and
Manuel Castellet
Carles Casacuberta
Affiliation:
Departament d'àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain
Manuel Castellet
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain
Get access Rights & Permissions [Opens in a new window]

Extract

In a series of papers [13, 14, 15], Hilton introduced the terminology relative group to denote a group epimorphism ∈:G↠Q, and relative space to denote a map ƒ:E→B between connected spaces inducing an epimorphism of fundamental groups. He pointed out the desirability of relativizing the theory of P-localization of nilpotent groups and spaces developed in [17], and carried out the algebraic part of this project in [14, 16]. The homotopy-theoretic part was settled by Llerena in [18, 19].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 551 - 564
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Adams, J. F.. Localisation and completion. Lecture Notes, University of Chicago (1975).Google Scholar
[2]Baumslag, G.. Some aspects of groups with unique roots. Ada Math. 104 (1960), 217–303.Google Scholar
[3]Bousfield, A. K. and Kan, D. M.. Homotopy Limits, Completions and Localizations. Lecture Notes in Math. vol. 304 (Springer-Verlag, 1972).CrossRefGoogle Scholar
[4]Casacuberta, C.. The behaviour of homology in the localization of finite groups. Canad. Math. Bull. 34 (1991), 311–320.CrossRefGoogle Scholar
[5]Casacuberta, C. and Peschke, G.. Localizing with respect to self maps of the circle. Trans. Amer. Math. Soc., to appear.Google Scholar
[6]Casacuberta, C., Peschke, G. and Pfenniger, M.. Sur la localisation dans les catégories avec une application à la tháorie de l'homotopie. C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 207–210.Google Scholar
[7]Casacuberta, C., Peschke, G. and Pfenniger, M.. Orthogonal pairs in categories and localization. In Proc. Adams Memorial Symposium, London Math. Soc. Lecture Note Ser. no. 175 (Cambridge University Press, 1992), pp. 211–223.Google Scholar
[8]Cassidy, C. and Lévesque, M.. On some closure-preserved properties Arch. Math. (Basel) 48 (1987), 105–108.CrossRefGoogle Scholar
[9]Freyd, P. J. and Kelly, G. M.. Categories of continuous functors (I). J. Pure Appl. Algebra 2 (1972), 169–191.CrossRefGoogle Scholar
[10]Gabriel, P. and Ulmer, F.. Lokal Präsentierbare Kategorien. Lecture Notes in Math. vol. 221 (Springer-Verlag, 1971).CrossRefGoogle Scholar
[11]García Rodicio, A.. Métodos homológicos en grupos P-locales. Ph.D. Thesis, Universidad de Santiago de Compostela (1986).Google Scholar
[12]Hilton, P.. Nilpotent actions on nilpotent groups. In Algebra and Logic, Lecture Notes in Math. vol. 450 (Springer-Verlag, 1975), pp. 174–196.CrossRefGoogle Scholar
[13]Hilton, P.. Groupes relatifs et espaces relatifs. In Proc. VI Congrès du Groupement des Mathématiciens d'expression Latine, Actualités Mathématiques (Gauthiers-Villars, 1982), pp. 167–178.Google Scholar
[14]Hilton, P.. Relative nilpotent groups. In Categorical Aspects of Topology and Analysis, Lecture Notes in Math. vol. 915 (Springer-Verlag, 1982), pp. 136–147.CrossRefGoogle Scholar
[15]Hilton, P.. Nilpotency in group theory and topology. Publ. Mat. 26 (1982), 47–78.CrossRefGoogle Scholar
[16]Hilton, P.. Localization of crossed modules. In Séminaire d'algèbre Paul Dubreil et Marie-Paule Malliavin, Lecture Notes in Math. vol. 1029 (Springer-Verlag, 1983), pp. 311–324.CrossRefGoogle Scholar
[17]Hilton, P., Mislin, G. and Roitberg, J.. Localization of Nilpotent Groups and Spaces. North-Holland Math. Studies no. 15 (North-Holland, 1975).Google Scholar
[18]Llerena, I.. Localization of nilpotent fibre maps. Collect. Math. 33 (1982), 177–185.Google Scholar
[19]Llerena, I.. Localization of fibrations with nilpotent fibre. Math. Z. 188 (1985), 397–410.CrossRefGoogle Scholar
[20]Peschke, G.. Localizing groups with action. Publ. Mat. 33 (1989), 227–234.CrossRefGoogle Scholar
[21]Reynol, A.. P-localization of some classes of groups. Ph.D. thesis, IME, Universidade de Sao Paulo (1987).Google Scholar
[22]Ribenboim, P.. Torsion et localisation de groupes arbitraires. In Séminaire d'algèbre Paul Dubreil, Lecture Notes in Math. vol. 740 (Springer-Verlag, 1979), pp. 444–456.CrossRefGoogle Scholar
[23]Ribenboim, P.. Equations in groups, with special emphasis on localization and torsion (I). Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. la (8) 19 (1987), 23–60.Google Scholar
[24]Ribenboim, P.. Equations in groups, with special emphasis on localization and torsion (II). Portugal. Math. 44 (1987), 417–445.Google Scholar
[25]Serre, J.-P.. Arbres, Amalgames, SL2. Astérisque no. 46 (Soc. Math. France, 1977).Google Scholar