For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms are permutable.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1218–1226, September, 2011.
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Derech, V.D. Structure of a finite commutative inverse semigroup and a finite bundle for which the inverse monoid of local automorphisms is permutable. Ukr Math J 63, 1390–1399 (2012). https://doi.org/10.1007/s11253-012-0586-4
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DOI: https://doi.org/10.1007/s11253-012-0586-4