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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.


Geometric spaces Hypergroup strongly regular relation

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Author Biographies

Saeed Mirvakili, Depratment of Mathematics, Payame Noor University, Tehran, Iran

Associate Professor of Mathematics, Payame Noor University, Tehran, Iran

Peyman Ghiasvand, Payame Noor University

Depratment of Mathematics, Payame Noor University, Tehran, Iran
How to Cite
Mirvakili, S., & Ghiasvand, P. (2018). Transitivity of The delta^n-Relation in Hypergroups. Journal of the Indonesian Mathematical Society, 24(2), 36–46.


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