Sur le groupe des automorphismes d’un groupoïde

Abstract

In some of the articles quoted in the present paper it is proved that every group can be represented as the automorphism group of a groupoid. The

On the hypergroups with four proper pairs and without scalars

“…In [3], [4], [5], Freni, Gutan C., Gutan M. and Sureau Y. have determined all the hypergroups which have at the most three proper pairs.…”

“…The corresponding left case can be c.btained for symmetry. (We remember that if the set of scalars is non-empty, then the set of left scalars is equal to the set of right scalars (see [3]). This case is handled in other papers from the same authors ).…”

“…has not been used. The complexity of the cases studied in the subsequent sections and the final aim of the authors (to find the hypergroups which have exactly four proper pairs) in accordance with the papers [3], [4], [5], have prevented them from verifying if in some cases the hypergroups could be found without the.use of (1.2). So, to find all semihypergroups with at most four proper pairs remains an open question.…”