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Classification of finite structurally uniform nilsemigroups

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Abstract

A finite semigroup S is called structurally uniform if any two subsemigroup of S are isomorphic whose heights in the partially ordered set of all subsemigroups of S are equal. Note that this class contains the class of all finite semigroups for which the inverse monoid of local automorphisms is congruence permutable. In this paper, we present a classification of finite structurally uniform nilsemigroups.

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Acknowledgements

To significantly improve the article, the referee did a great job. The author is grateful to him/her for this.

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Authors and Affiliations

  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. Classification of finite structurally uniform nilsemigroups. Semigroup Forum 106, 394–402 (2023). https://doi.org/10.1007/s00233-023-10341-6

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  • DOI: https://doi.org/10.1007/s00233-023-10341-6

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