TY - JOUR AU - Mirvakili, Saeed AU - Ghiasvand, Peyman PY - 2018/05/18 Y2 - 2024/03/29 TI - Transitivity of The delta^n-Relation in Hypergroups JF - Journal of the Indonesian Mathematical Society JA - JIMS VL - 24 IS - 2 SE - Articles DO - 10.22342/jims.24.2.524.36-46 UR - https://jims-a.org/index.php/jimsa/article/view/524 SP - 36-46 AB - The $\delta^n$-relation was introduced by Leoreanu-Fotea et. al.\cite{130}. In this article, we introduce the concept of$\delta^{n}$-heart of a hypergroup and we determine necessary andsufficient conditions for the relation $\delta^{n}$ to betransitive. Moreover, we determine a family $P_{\sigma}(H)$ ofsubsets of a hypergroup $H$ and we give sufficient conditionssuch that the geometric space $(H, P_{\sigma}(H))$ is stronglytransitive and the relation $\delta^n$ is transitive. ER -