Automorphism groups of superextensions of finite monogenic semigroups

Taras O. Banakh, Volodymyr M. Gavrylkiv


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 \(* : X\times X \to X\) can be extended to an associative binary operation \(*: \lambda(X)\times\lambda(X)\to\lambda(X)\). 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 \(\leq 5\).


monogenic semigroup, maximal linked upfamily, superextension, automorphism group

Full Text:



  • There are currently no refbacks.