The Polypermutation Group of an Associative Ring

Abstract

We study permutation polynomials through the device of the \emph{polypermutation group} of an associative ring $R$, denoted by $\mathrm{Pgr}(R)$. We derive some basic properties and compute the cardinality of $\mathrm{Pgr}(\mathbb{Z}/p^k)$ when $p\ge k$. We use this computation to determine the structure of $\mathrm{Pgr}(\mathbb{Z}/p^2)$.

arXiv comment9 pages, comments welcome. Updated version: mostly unchanged, minor typographical errors fixed, now has been accepted for publication in Contemporary Mathematics