Geodesic
Automorphism groups of superextensions of finite monogenic semigroups
Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 165-190.

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A family $\mathcal L$ of subsets of a set $X$ is called linked if $A\cap B\ne\emptyset$ for any $A,B\in\mathcal L$. A linked family $\mathcal M$ of subsets of $X$ is maximal linked if $\mathcal M$ coincides with each linked family $\mathcal L$ on $X$ that contains $\mathcal M$. The superextension $\lambda(X)$ of $X$ consists of all maximal linked families on $X$. Any associative binary operation $*\colon X\times X \to X$ can be extended to an associative binary operation $*\colon \lambda(X)\times\lambda(X)\to\lambda(X)$. In the paper we study automorphisms of the superextensions of finite monogenic semigroups and characteristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality $\leq 5$.
Keywords: monogenic semigroup, maximal linked upfamily, superextension
Mots-clés : automorphism group. 
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Taras Banakh; Volodymyr Gavrylkiv. Automorphism groups of  superextensions of finite monogenic semigroups. Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 165-190. http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a2/

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