Classification of finite semigroups for which the inverse monoid of local automorphisms is a Δ-semigroup

Abstract

A semigroup S is called a ∆-semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of the semigroup S is defined as an isomorphism between its two subsemigroups. The set of all local automorphisms of the semigroup S relative to the operation of composition forms an inverse monoid of local automorphisms. In the current paper we present a classification of all finite semigroups for which the inverse monoid of local automorphisms is a ∆-semigroup.