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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 5, pp. 610–624, May, 2016.
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Derech, V.D. Classification of Finite Nilsemigroups For Which the Inverse Monoid of Local Automorphisms is a Permutable Semigroup. Ukr Math J 68, 689–706 (2016). https://doi.org/10.1007/s11253-016-1251-0
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DOI: https://doi.org/10.1007/s11253-016-1251-0