Stefano Fioravanti – Expansions of abelian squarefree groups

Johannes Kepler University Linz

We investigate finitary functions from
to
for a squarefree number . We show that the lattice of all clones on the squarefree set
which contain the addition of
is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattices of all
-linearly closed clonoids,
, to the power, where
. Furthermore, we prove that these clones can be generated by a set of functions of arity at most
.