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Complete Classification of Finite Semigroups for Which the Inverse Monoid of Local Automorphisms is a Permutable Semigroup

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Ukrainian Mathematical Journal Aims and scope

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 the semigroup S with respect to the 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.

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References

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Authors and Affiliations

  1. Vinnytsya National Technical University, Vinnytsya, Ukraine

    V. D. Derech

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  1. V. D. Derech
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 11, pp. 1571–1578, November, 2016.

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Derech, V.D. Complete Classification of Finite Semigroups for Which the Inverse Monoid of Local Automorphisms is a Permutable Semigroup. Ukr Math J 68, 1820–1828 (2017). https://doi.org/10.1007/s11253-017-1330-x

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  • DOI: https://doi.org/10.1007/s11253-017-1330-x

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