Abstract.
We study existence and possible uniqueness of special semihypergroups of type U on the right. In particular, we prove that there exists a unique proper semihypergroup of this kind having order 6, apart of isomorphisms; the least order for a hypergroup of type U on the right to have a stable part which is not a subhypergroup is 9; and the minimal cardinality of a proper semihypergroup of that kind whose heart and derived semihypergroup are proper and nontrivial is 12.
Contextually, we analyze properties of the kernel of homomorphisms g : H ↦ G, where H is a finite semihypergroup of type U on the right and G is a group. In this way, we obtain results that are immediately applicable both to the heart and to the derived of such semihypergroups.
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Fasino, D., Freni, D. Minimal Order Semihypergroups of Type U on the Right. MedJM 5, 295–314 (2008). https://doi.org/10.1007/s00009-008-0151-4
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DOI: https://doi.org/10.1007/s00009-008-0151-4