SEMIGROUP DISTANCES OF FINITE GROUPOIDS - Batíková, Barbora; Dvořáková, Šárka; Trch, Milan (Italian Journal of Pure and Applied Mathematics, 2014)
The simplest cases of non-associative groupoids are presented by groupoids (so called SH-groupoids) having just one non-associative (ordered) triple of elements. In this paper, only SH-groupoids having the simplest possible non-associative triple (a, a, a) are investigated. For each positive integer n finite SH-groupoids En(·) generated by at most two elements are constructed and their semigroup distances are described. It is proved that there are finite non-associative groupoids having their semigroup distance equal just to the arbitrary given positive integer n.