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 theinverse monoid of local automorphisms is permutable.Полугруппа $S$ называется перестановочной, если для любой пары конгруэнций $ρ$, $σ$ на $S$ имеет место равенство $ρ ° σ = σ ° ρ$.