%0 Journal Article
%T Applicazioni (h,A)-lineari omomorfismi di M_A-ipergruppoidi
%A Domenico Freni
%J Le Matematiche
%D 1999
%I University of Catania
%X In the papers [9], [10] we introduced and studied M_¦Ë -hypergroupoids; also, we obtained some results on the automorphism group of a G_ ¦Ë -hypergroupoid. In particular, given a group G and one of its element ¦Ë, we proved that the automorphisms of the  corresponding G_¦Ë -hypergroupoid are the one-one maps f : G ¡ú G  which are ¦Ë-linea. A natural generalization of the notion of ¦Ë-linearity is the notion of (h, A, B)-linearity, introduced in the present paper. Theorem 1.7 provides the existence and uniqueness of a (h, A, B)-linear map. Theorem 2.3 gives the cardinality of the group ¦«(G A ) of complete, bijective (h, A)-linear maps. In Theorem 2.7 we prove that ¦«(G A ) is a semi-direct product. The notion of M_A -hypergroupoid is defned in the last section, via group actions on sets. We also study their homomorphisms and prove that the M_A -hypergroupoid is a hypergroup or a join-space according to the set A being a stable part or a subgroup of G.
%U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/337