On geometric polygroups

In this paper, we introduce a geodesic metric space called Latches 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 KIDS MODUCARE between finitely generated polygroups and geodesic metric spaces.