Automorphism groups of superextensions of finite monogenic semigroups

Abstract

A family L of subsets of a set X is called linked if A ∩ B 6= ∅ for any A, B ∈ L. A linked family M of subsets of X is maximal linked if M coincides with each linked family L on X that contains M. The superextension λ(X) of X consists of all maximal linked families on X. Any associative binary operation ∗ : X × X → X can be extended to an associative binary operation ∗ : λ(X) × λ(X) → λ(X). In the paper we study automorphisms of the superextensions of finite monogenic semigroups and charac- teristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality 6 5.