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Bousfield localization as an algebraic closure of groups

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Abstract

We show that the notion ofHZ-local groups due to A. Bousfield which is based on considerations from algebraic topology can be defined and understood in terms of solubility of certain systems of equations overG.

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References

  1. A. K. Bousfield,Homological localizations for groups and π-modules, Memoirs Am. Math. Soc.186 (1977).

  2. A. K. Bousfield and D. M. Kan,Homotopy limits, completions and localizations, Lecture Notes in Math. Vol. 304, Springer-Verlag, Berlin, 1972.

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  3. J. Howie,How to generalize one relator group theory, inCombinatorial Group Theory and Topology (S. Gersten and J. Stallings, eds.) Ann. Math. Studies No. 111, Princeton University Press, 1987.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    E. Dror Farjoun, K. Orr & S. Shelah

  2. Department of Mathematics, University of Chicago, Chicago, Illinois, USA

    E. Dror Farjoun, K. Orr & S. Shelah

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  1. E. Dror Farjoun
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  2. K. Orr
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  3. S. Shelah
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Farjoun, E.D., Orr, K. & Shelah, S. Bousfield localization as an algebraic closure of groups. Israel J. Math. 66, 143–153 (1989). https://doi.org/10.1007/BF02765889

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  • DOI: https://doi.org/10.1007/BF02765889

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