The arithmetic of polynomial maps over a group

I introduce the article

S. D. Scott, The arithmetic of polynomial maps over a group and the structure of certain permutational polynomial groups. I, Monatsh. Math. 73 (1969), 250-267.

We discuss polynomial maps of a finite group G into itself. We find the order of the semigroup, under composition, of all polynomial maps of G into G in terms of two invariants. One of these invariants is used again in finding the order of the group under composition of all polynomial maps of G onto G. Next the problem of finding all polynomial maps over a cartesian product is dealt with. Also the problem of finding those maps which are onto is discussed.