Archiv der Mathematik

, Volume 109, Issue 5, pp 407–412 | Cite as

Metric ultraproducts of classical groups

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Abstract

Simple non-discrete metric ultraproducts of classical groups are geodesic spaces with respect to a natural metric.

Keywords

Classical groups Metric ultraproducts 

Mathematics Subject Classification

20G15 11U07 54E50 

References

  1. 1.
    J. Dieudonné, Sur les générateurs des groupes classiques, Summa Brasil. Math. 3 (1955), 149–179.MathSciNetMATHGoogle Scholar
  2. 2.
    G. Elek and E. Szabó, Hyperlinearity, essentially free actions and \(L^2\)-invariants. The sofic property, Math. Ann. 332 (2005), 421–441.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    P. Kleidman and M. Liebeck, The Subgroup Structure of the Finite Classical Groups, London Mathematical Society Lecture Note Series, 129, Cambridge University Press, Cambridge, 1990.Google Scholar
  4. 4.
    N. Nikolov, Strange images of profinite groups, arXiv:0901.0244v3 [math.GR].
  5. 5.
    A. Stolz and A. Thom, On the lattice of normal subgroups in ultraproducts of compact simple groups, Proc. London Math. Soc. (3) 108 (2014), 73–102.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    A. Thom and J. S. Wilson, Metric ultraproducts of finite simple groups, C. R. Math. Acad. Sci. Paris 352 (2014), 463–466.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    A. Thom and J. S. Wilson, Some geometric properties of metric ultraproducts of finite simple groups, arXiv:1606.03863 [math.GR].
  8. 8.
    P. Wantiez, Limites d’espaces métriques et ultraproduits, In: Méthodes et analyse non standard, 141–168, Cahiers Centre Logique, 9, Acad.-Bruylant, Louvain-la-Neuve, 1996.Google Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Christ’s CollegeCambridgeUnited Kingdom

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