Applicazioni (h,A)-lineari omomorfismi di M_A-ipergruppoidi

Abstract

In the papers [9], [10] we introduced and studied M_λ -hypergroupoids; also, we obtained some results on the automorphism group of a G_ λ -hypergroupoid. In particular, given a group G and one of its element λ, we proved that the automorphisms of the  corresponding G_λ -hypergroupoid are the one-one maps f : G → G  which are λ-linea.

A natural generalization of the notion of λ-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 Λ(G A ) of complete, bijective (h, A)-linear maps. In Theorem 2.7 we prove that Λ(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.