TY - JOUR
ID - 2196
TI - Geometric Hypergroups
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Al Tahan, M.
AU - Davvaz, B.
AD - Department of Mathematics, Lebanese International University, Bekaa, Lebanon.
AD - Department of Mathematics, Yazd University, Yazd, Iran.
Y1 - 2022
PY - 2022
VL - 9
IS - 2
SP - 241
EP - 257
KW - Cayley graph
KW - hypergroup
KW - geometric hypergroup
DO - 10.22044/jas.2021.9981.1493
N2 - The aim of this paper is to extend the notion of geometric groups to geometric hypergroups and to investigate the interaction between algebraic and geometric properties of hypergroups. In this regard, we first define a metric structure on hypergroups via word metric and present some examples on it by using generalized Cayley graphs over hypergroups. Then we study a large scale of geometry with respect to the structure of hypergroups and we prove that metric spaces of finitely generated hypergroups coming from different generating sets are quasi-isometric.
UR - http://jas.shahroodut.ac.ir/article_2196.html
L1 - http://jas.shahroodut.ac.ir/article_2196_429071f73af8f14407a78631514f916a.pdf
ER -