Let G(n) denote the class of hypergroups of type U on the right of size n with bilateral scalar identity. In this paper we consider the hypergroups (H, o). G(7) which own a proper and non- trivial subhypergroup h. For these hypergroups we prove that h is closed if and only if ( H - h) o (H - h) = h. Moreover we consider the set G(7) of hypergroups in G(7) that own the above property. On this set, we introduce a partial ordering induced by the inclusion of hyperproducts. This partial ordering allows us to give a complete characterization of hypergroups in G(7) on the basis of a small set of minimal hypergroups, up to isomorphisms. This analysis gives a partial (negative) answer to a problem raised in [5] concerning the existence in G(n) of proper hypergroups having singletons as special hyperproducts.
On strongly conjugable extensions of hypergroups of type U with scalar identity
DE SALVO, Mario;LO FARO, Giovanni
2013-01-01
Abstract
Let G(n) denote the class of hypergroups of type U on the right of size n with bilateral scalar identity. In this paper we consider the hypergroups (H, o). G(7) which own a proper and non- trivial subhypergroup h. For these hypergroups we prove that h is closed if and only if ( H - h) o (H - h) = h. Moreover we consider the set G(7) of hypergroups in G(7) that own the above property. On this set, we introduce a partial ordering induced by the inclusion of hyperproducts. This partial ordering allows us to give a complete characterization of hypergroups in G(7) on the basis of a small set of minimal hypergroups, up to isomorphisms. This analysis gives a partial (negative) answer to a problem raised in [5] concerning the existence in G(n) of proper hypergroups having singletons as special hyperproducts.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
