Automorphisms of semigroups of k-linked upfamilies

Abstract

A family A of non-empty subsets of a set X is called an upfamily if for each set A ∈ A any set B ⊃ A belongs to A.Any associative binary operation * : X × X → X can be extended to an associative binary operation * : N k (X)×N k (X) → N k (X). In the paper, we study automorphisms of the extensions of groups, finite monogenic semigroups and describe the automorphism groups of extensions of null semigroups, almost null semigroups, right zero semigroups and left zero semigroups.