Tue, 13 Oct 2020, 1 pm MDT

We investigate ﬁnitary functions from Z_n to Z_n for a squarefree number n. We show that for squarefree n the lattice of all clones on Z_n which contain the addition of Z_n is ﬁnite and we provide an upper bound for the cardinality of this lattice. Furthermore, we prove that these clones can be generated by functions of arity at most the greatest prime factor of n.