Isometry groups of non standard metric products

Bogdana Oliynyk

Open Mathematics (2013)

  • Volume: 11, Issue: 2, page 264-273
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Bogdana Oliynyk. "Isometry groups of non standard metric products." Open Mathematics 11.2 (2013): 264-273. <http://eudml.org/doc/269566>.

@article{BogdanaOliynyk2013,
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.},
author = {Bogdana Oliynyk},
journal = {Open Mathematics},
keywords = {Isometry group; Metric space; Non standard metric product; Direct product; Wreath product; isometry group; metric space; non standard metric product; direct product; wreath product},
language = {eng},
number = {2},
pages = {264-273},
title = {Isometry groups of non standard metric products},
url = {http://eudml.org/doc/269566},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Bogdana Oliynyk
TI - Isometry groups of non standard metric products
JO - Open Mathematics
PY - 2013
VL - 11
IS - 2
SP - 264
EP - 273
AB - 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.
LA - eng
KW - Isometry group; Metric space; Non standard metric product; Direct product; Wreath product; isometry group; metric space; non standard metric product; direct product; wreath product
UR - http://eudml.org/doc/269566
ER -

References

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  1. [1] Avgustinovich S., Fon-Der-Flaass D., Cartesian products of graphs and metric spaces, European J. Combin., 2000, 21(7), 847–851 http://dx.doi.org/10.1006/eujc.2000.0401 Zbl0976.54027
  2. [2] Bernig A., Foertsch T., Schroeder V., Non standard metric products, Beiträge Algebra Geom., 2003, 44(2), 499–510 Zbl1049.54009
  3. [3] Chen C.-H., Warped products of metric spaces of curvature bounded from above, Trans. Amer. Math. Soc., 1999, 351(12), 4727–4740 http://dx.doi.org/10.1090/S0002-9947-99-02154-6 Zbl0979.53035
  4. [4] Gawron P.W., Nekrashevych V.V., Sushchansky V.I., Conjugation in tree automorphism groups, Internat. J. Algebra Comput., 2001, 11(5), 529–547 http://dx.doi.org/10.1142/S021819670100070X Zbl1030.20015
  5. [5] Moszynska M., On the uniqueness problem for metric products, Glas. Mat. Ser. III, 1992, 27(47)(1), 145–158 Zbl0802.54020
  6. [6] Oliynyk B., Wreath product of metric spaces, Algebra Discrete Math., 2007, 4, 123–130 Zbl1156.28310
  7. [7] Kalužnin L.A., Beleckij P.M., Fejnberg V.Z., Kranzprodukte, Teubner-Texte Math., 101, Teubner, Leipzig, 1987 
  8. [8] Schoenberg I.J., Metric spaces and completely monotone functions, Ann. Math., 1938, 39(4), 811–841 http://dx.doi.org/10.2307/1968466 Zbl64.0617.03

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