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