About this article
Published Online: Apr 09, 2020
Page range: 17 - 33
Received: May 04, 2019
Accepted: Jul 23, 2019
DOI: https://doi.org/10.2478/auom-2020-0002
Keywords
© 2020 F. Arabpur et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
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.