Transitivity of The delta^n-Relation in Hypergroups

Saeed Mirvakili (Depratment of Mathematics, Payame Noor University, Tehran, Iran)
Peyman Ghiasvand (Payame Noor University)

Journal of the Indonesian Mathematical Society
Volume 24 Number 2 (October 2018)

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.