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Automorphisms of semigroups of k-linked upfamilies

  • Volodymyr M. Gavrylkiv
Article

Abstract

A family \( \mathcal{A} \) of non-empty subsets of a set X is called an upfamily, if, for each set \( A\in \mathcal{A} \); any set B ⊃ A belongs to \( \mathcal{A} \). An upfamily \( \mathrm{\mathcal{L}} \) is called k-linked, if \( \cap \mathrm{\mathcal{F}}\ne \varnothing \) for any subfamily \( \mathrm{\mathcal{F}}\subset \mathrm{\mathcal{L}} \) of cardinality \( \left|\mathrm{\mathcal{F}}\right|\le k \). The extension Nk(X) consists of all k-linked upfamilies on X. Any associative binary operation ∗ : X × X → X can be extended to an associative binary operation ∗ : Nk(X) × Nk(X) → Nk(X). Here, we study automorphisms of the extensions of groups and finite monogenic semigroups. We also describe the automorphism groups of extensions of null semigroups, almost null semigroups, right zero semigroups and left zero semigroups.

Keywords

Semigroup k-linked upfamily automorphism group 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vasyl Stefanyk Precarpathian National UniversityIvano-FrankivskUkraine

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