Geodesic
Infinitely iterated wreath products of metric spaces
Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 48-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

The construction of the finitary wreath product of metric spaces and its completion, the infinitely iterated wreath product of metric spaces are introduced. They full isometry groups are described. Some properties and examples of these constructions are considered.
Keywords: Metric space, Wreath product, Isometry group. 
@article{ADM_2013_15_1_a5,
     author = {B. Oliynyk},
     title = {Infinitely iterated wreath products of metric spaces},
     journal = {Algebra and discrete mathematics},
     pages = {48--62},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a5/}
}
TY  - JOUR
AU  - B. Oliynyk
TI  - Infinitely iterated wreath products of metric spaces
JO  - Algebra and discrete mathematics
PY  - 2013
SP  - 48
EP  - 62
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a5/
LA  - en
ID  - ADM_2013_15_1_a5
ER  - 
%0 Journal Article
%A B. Oliynyk
%T Infinitely iterated wreath products of metric spaces
%J Algebra and discrete mathematics
%D 2013
%P 48-62
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a5/
%G en
%F ADM_2013_15_1_a5
B. Oliynyk. Infinitely iterated wreath products of metric spaces. Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 48-62. http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a5/

[1] L. M. Blumenthal, “Remarks concerning the euclidean four-point property”, Erg. Math. Kolloqu., 1936, no. 7, 8–10

[2] I. J. Schoenberg, “Metric spaces and completely monotone functions”, Ann. Math. (2), 39 (1938), 811–841 | DOI | MR

[3] J. von Neumann, I. J. Schoenberg, “Fourier integrals and metric geometry”, Trans. Amer. Math. Soc., 50 (1941), 226–251 | DOI | MR

[4] H. Maehara, “Metric transforms of finite spaces and connected graphs”, Discrete Math., 61 (1986), 235–246 | DOI | MR | Zbl

[5] R. I. Grigorchuk, V. V. Nekrashevich, V. I. Sushchanskii, “Automata, dynamical systems, and groups”, Proc. Steklov Inst. Math., 231, 2000, 128–203 (Russian) | MR | Zbl

[6] L. Babai, “Automorphism groups, isomorphism, reconstruction”, Handbook of Combinatorics, eds. R. L. Graham, M. Grotschel, L. Lovasz, North-Holland, Amsterdam, 1995, 1447–1540 | MR | Zbl

[7] B. Oliynyk, “Wreath product of metric spaces”, Algebra Discrete Math., 2007, no. 4, 123–130 | MR | Zbl

[8] L. A. Kaluzhnin, P. M. Beletskij, V. T. Fejnberg, Kranzprodukte, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1987 | MR | Zbl

[9] R. Frucht, “Herstellung von Graphen mit vorgegebener abstrakter Gruppe”, Compos. Math., 6 (1938), 239–250 | MR

[10] B. Olijnyk, “Isomorphic embeddings of finite metric spaces into Hamming spaces”, Mat. Stud., 8:2 (1997), 176–179 | MR | Zbl

[11] P. J. Cameron, S. Tarzi, “Limits of cubes”, Topology Appl., 155:14 (2008), 1454–1461 | DOI | MR | Zbl

[12] V. I. Sushchanskij, “Representation of finitely approximable groups by isometries of uniform ultrametric spaces of finite width”, Dokl. Akad. Nauk Ukr. SSR, Ser. A, 1988, no. 4, 19–22 (Russian) | Zbl

[13] J. Kigami, Analysis on Fractals, Cambridge University Press, 2001 | MR | Zbl

[14] V. Nekrashevych, Self-similar groups, Mathematical Surveys and Monographs, 117, Amer. Math. Soc., Providence, RI, 2005 | DOI | MR | Zbl