Abstract
We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Avgustinovich S., Fon-Der-Flaass D., Cartesian products of graphs and metric spaces, European J. Combin., 2000, 21(7), 847–851
Bernig A., Foertsch T., Schroeder V., Non standard metric products, Beiträge Algebra Geom., 2003, 44(2), 499–510
Chen C.-H., Warped products of metric spaces of curvature bounded from above, Trans. Amer. Math. Soc., 1999, 351(12), 4727–4740
Gawron P.W., Nekrashevych V.V., Sushchansky V.I., Conjugation in tree automorphism groups, Internat. J. Algebra Comput., 2001, 11(5), 529–547
Moszynska M., On the uniqueness problem for metric products, Glas. Mat. Ser. III, 1992, 27(47)(1), 145–158
Oliynyk B., Wreath product of metric spaces, Algebra Discrete Math., 2007, 4, 123–130
Kalužnin L.A., Beleckij P.M., Fejnberg V.Z., Kranzprodukte, Teubner-Texte Math., 101, Teubner, Leipzig, 1987
Schoenberg I.J., Metric spaces and completely monotone functions, Ann. Math., 1938, 39(4), 811–841
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Oliynyk, B. Isometry groups of non standard metric products. centr.eur.j.math. 11, 264–273 (2013). https://doi.org/10.2478/s11533-012-0132-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-012-0132-5