Closed sets of finitary functions between finite fields of coprime order

We investigate the finitary functions from a finite field Fq to the finite field Fp, where p and q are powers of different primes. An (Fp, Fq) -linearly closed clonoid is a subset of these functions which is closed under composition from the right and from the left with linear mappings. We give a characterization of these subsets of functions through the invariant subspaces of the vector space FpFq\{0} with respect to a certain linear transformation with minimal polynomial xq-1- 1. Furthermore we prove that each of these subsets of functions is generated by one unary function. © 2020, The Author(s).