Isometry groups of non standard metric products
Bogdana Oliynyk
Open Mathematics, Tome 11 (2013), p. 264-273 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:269566
@article{bwmeta1.element.doi-10_2478_s11533-012-0132-5,
     author = {Bogdana Oliynyk},
     title = {Isometry groups of non standard metric products},
     journal = {Open Mathematics},
     volume = {11},
     year = {2013},
     pages = {264-273},
     zbl = {1266.54074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0132-5}
}
Bogdana Oliynyk. Isometry groups of non standard metric products. Open Mathematics, Tome 11 (2013) pp. 264-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0132-5/

[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 | Zbl 0976.54027

[2] Bernig A., Foertsch T., Schroeder V., Non standard metric products, Beiträge Algebra Geom., 2003, 44(2), 499–510 | Zbl 1049.54009

[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 | Zbl 0979.53035

[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 | Zbl 1030.20015

[5] Moszynska M., On the uniqueness problem for metric products, Glas. Mat. Ser. III, 1992, 27(47)(1), 145–158 | Zbl 0802.54020

[6] Oliynyk B., Wreath product of metric spaces, Algebra Discrete Math., 2007, 4, 123–130 | Zbl 1156.28310

[7] Kalužnin L.A., Beleckij P.M., Fejnberg V.Z., Kranzprodukte, Teubner-Texte Math., 101, Teubner, Leipzig, 1987

[8] Schoenberg I.J., Metric spaces and completely monotone functions, Ann. Math., 1938, 39(4), 811–841 http://dx.doi.org/10.2307/1968466 | Zbl 64.0617.03