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Complete classification of finite semigroups for which the inverse monoid of local automorphisms is a \(\varDelta \)-semigroup

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Abstract

A semigroup S is called a \(\varDelta \)-semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of a semigroup S is defined as an isomorphism between its two subsemigroups. The set of all local automorphisms of a semigroup S relative to the operation of composition forms an inverse monoid of local automorphisms. We present a classification of all finite semigroups for which the inverse monoid of local automorphisms is a \(\varDelta \)-semigroup.

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Acknowledgements

The author expresses his sincere gratitude to the referee for an extremely detailed analysis of the article. Moreover, the referee gave his/her versions of the proof of all the main statements of the article, and the author used them.

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  1. Department of Mathematics, Faculty of Information Technologies and Computer Engineering, Vinnytsia National Technical University, 95 Khmelnytske Shose, Vinnytsia, 21021, Ukraine

    V. D. Derech

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  1. V. D. Derech
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Correspondence to V. D. Derech.

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Communicated by Mark V. Lawson.

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Derech, V.D. Complete classification of finite semigroups for which the inverse monoid of local automorphisms is a \(\varDelta \)-semigroup. Semigroup Forum 102, 397–407 (2021). https://doi.org/10.1007/s00233-020-10159-6

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  • DOI: https://doi.org/10.1007/s00233-020-10159-6

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