Engel groups derived from hypergroups

This paper deals with hypergroups, as a generalization of classical groups. An important tool in the theory of hyperstructures is the fundamental relation, which brings us into the classical algebra. In this paper we introduce the smallest equivalence relation xi* on a given hypergroup H such that the quotient H/xi*, the set of all equivalence classes, is an Engel group. We will characterize Engle groups via strongly regular relations and several results on the topic are presented. (C) 2014 Elsevier Ltd. All rights reserved.