A semigroup $S$ is called permutable if $\rho \circ \sigma = \sigma \circ \rho$. for any pair of congruences $\rho, \sigma$ on $S$.
A local automorphism of semigroup $S$ is defined as an isomorphism between two of its subsemigroups. The set of all local automorphisms of the semigroup $S$ with respect to an ordinary operation of composition of binary relations forms an inverse monoid of local automorphisms. We present a complete classification of finite semigroups for which the inverse monoid of local
automorphisms is permutable.
Citation Example:Derech V. D. Complete classification of finite semigroups for which the inverse monoid of
local automorphisms is a permutable semigroup // Ukr. Mat. Zh. - 2016. - 68, № 11. - pp. 1571-1578.
