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Abstract
In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.
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Details
1 Mathematics Department, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
2 Department of Mathematics and Physics, University of Defence in Brno Kounicova 65, 662 10, Brno, Czech Republic