Classification of Finite Nilsemigroups For Which the Inverse Monoid of Local Automorphisms is a Permutable Semigroup

Abstract

A semigroup S is called permutable if $$ \rho $$ ◦ σ = σ ◦ $$ \rho $$ for any pair of congruences $$ \rho $$ , σ on S. A local automorphism of the semigroup S is defined as an isomorphism between two subsemigroups of this semigroup. The set of all local automorphisms of a semigroup S with respect to an ordinary operation of composition of binary relations forms an inverse monoid of local automorphisms. We present a classification of all finite nilsemigroups for which the inverse monoid of local automorphisms is permutable.