Complete classification of finite semigroups for which the inverse monoid of local automorphisms is a Δ-semigroup.

A semigroup S is called a Δ -semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of a semigroup S is defined as an isomorphism between its two subsemigroups. The set of all local automorphisms of a semigroup S relative to the operation of composition forms an inverse monoid of local automorphisms. We present a classification of all finite semigroups for which the inverse monoid of local automorphisms is a Δ -semigroup. [ABSTRACT FROM AUTHOR]