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.
