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 from H to 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.
Minimal order semihypergroups of type U on the right
FASINO, Dario;FRENI, Domenico
2008-01-01
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 from H to 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
