Description:
<jats:title>Abstract</jats:title><jats:p>Let <jats:italic>Z<jats:sub>n</jats:sub></jats:italic> be the factor ring of the integers mod <jats:italic>n</jats:italic> and <jats:italic>t</jats:italic> be a positive integer. In this paper some results are given on the structure of the semigroup of all mappings from <jats:italic>Z<jats:sub>n</jats:sub></jats:italic> into <jats:italic>Z<jats:sub>n</jats:sub></jats:italic> and on the structure of the group of all permutations on <jats:italic>Z<jats:sub>n</jats:sub></jats:italic>, which, for any <jats:italic>t</jats:italic> elements, can be represented by a polynomial function. If <jats:italic>n = ab</jats:italic> and <jats:italic>a, b</jats:italic> are relatively prime, then this (semi)group is isomorphic to the direct product of the respective (semi)groups for <jats:italic>a</jats:italic> and <jats:italic>b</jats:italic>. Thus it is sufficient to consider only the case where <jats:italic>n</jats:italic> = <jats:italic>p<jats:sup>e</jats:sup></jats:italic>, <jats:italic>p</jats:italic> being a prime. In this case it is proved, that the (semi)group is isomorphic to the wreath product of a certain sub(semi)group of the symmetric (semi)group on Z<jats:italic><jats:sub>p<jats:sup>e−1</jats:sup></jats:sub></jats:italic> by the symmetric (semi)group on <jats:italic>Z<jats:sub>p</jats:sub></jats:italic>. Some remarks on these sub(semi)groups are given.</jats:p><jats:p><jats:italic>Subject classification (Amer. Math. Soc. (MOS) 1970)</jats:italic>: 20 B 99, 13 B 25.</jats:p>