Geodesic
Tiling of groups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 69-72

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The following problem formulated by A. M. Vershik connected to several questions in the traectory theory of the finite generated groups pavements is being researched. The result is: let $G$ be decomposed into the free product of two nontrivial groups. Then for any finite subset $S$ of group $G$ there exists a finite subset $P$ of group $G$ including $S$ such that $G$ is being covered by nonintersected left translations of the set $P$. 
@article{ZNSL_1999_256_a5,
     author = {M. V. Zheludev},
     title = {Tiling of groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {69--72},
     publisher = {mathdoc},
     volume = {256},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a5/}
}
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M. V. Zheludev. Tiling of groups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 69-72. http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a5/