In this paper semigroups of contractions of metric spaces are considered. The semigroup of contractions of the wreath product of metric spaces is calculated.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1161, author = {Bogdana Oliynyk}, title = {Semigroup of Contractions of Wreath Products of Metric Spaces}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {30}, year = {2010}, pages = {35-43}, zbl = {1216.54008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1161} }
Bogdana Oliynyk. Semigroup of Contractions of Wreath Products of Metric Spaces. Discussiones Mathematicae - General Algebra and Applications, Tome 30 (2010) pp. 35-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1161/
[000] [1] F. Harary, On the group of the composition of two graphs, Duke Math J. 26 (1959), 47-51. doi: 10.1215/S0012-7094-59-02603-1
[001] [2] G. Sabidussi, The composition of graphs, Duke Math J. 26 (1959), 693-696. doi: 10.1215/S0012-7094-59-02667-5 | Zbl 0095.37802
[002] [3] I.J. Shoenberg, Metric spaces and completely monotone functions, The Annals of Mathematics 39 (4) (1938), 811-841. doi: 10.2307/1968466 | Zbl 64.0617.03
[003] [4] B. Oliynyk, Isometry groups of wreath products of metric spaces, Algebra and Discrete Mathematics 4 (2007), 123-130.
[004] [5] I.D. Meldrum, Wreath products of groups and semigroups, New York, Longman 1995. | Zbl 0833.20001
[005] [6] A. Oliinyk, On Free Semigroups of Automaton Transformations, Mathematical Notes 63 (2) (1998), 248-259. doi: 10.1007/BF02308761
[006] [7] J. Rhodes, Monoids acting on trees: Elliptic and wreath products and the holonomy theorem for arbitrary monoids with applications to infinite groups, Int. J. Algebra Comput. 1 (2) (1991), 253-279. doi: 10.1142/S0218196791000171 | Zbl 0797.20053