Classification of finite nilsemigroups for which the inverse monoid of local automorphisms is permutable semigroup - Derech, V. D. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
A semigroup S is called permutable if ρ ° σ = σ ° ρ for any pair of congruences ρ, 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. In the proposed paper, we present a classification of all finite nilsemigroups for which the inverse monoid of local automorphisms is permutable. Полугруппа S называется перестановочной, если для любой пары конгруэнций ρ, σ на S имеет место равенство ρ ° σ = σ ° ρ.