On finite structurally uniform semigroups

Abstract

A finite semigroup S is called structurally uniform if any two subsemigroup of S are isomorphic whose heights in the partially ordered set of all subsemigroups of S are equal. Note that this class contains the class of all finite semigroups for which the inverse monoid of local automorphisms is congruence permutable. In these notes, we give a brief overview of results about finite structurally uniform semigroups.