Classification of finite structurally uniform nilsemigroups

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 this paper, we present a classification of finite structurally uniform nilsemigroups.