Hypergroups of type U on the right of size five. Part two

Abstract

The hypergroups $H$ of type $U$ on the right can be classified in termsof the family $P_1=\{1\circ x\mid xınH\}$, where $1ınH$ isthe right scalar identity. If the size of $H$ is $5$, then $P_1$ canassume only $6$ possible values, three of which have been studied inthe first part of the paper. In this paper, we completelydescribe other two of the remaining possible cases:a)~$P_1=\{\{1\},\{2,3\},\{4\},\{5\}\}$;b)~$\text{Extra close brace or missing open brace}$.In these cases, $P_1$ is a partition of $H$ and the equivalencerelation associated to it is a regular equivalence on $H$.We find that, apart of isomorphisms, there are exactly $41$hypergroups in case~a), and $56$ hypergroup in case~b).