On geometric polygroups

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.

Keywords

• polygroup
• gcayley graph
• hyperaction
• geodesic metric space
• quasi-isometry
• primary 20n20
• secondary 20f65