On Schur p-groups of odd order

A finite group $G$ is called a Schur group if any $S$-ring over $G$ is associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. We prove that the groups ${\mathbb{Z}}_3\times {\mathbb{Z}}_{3^n}$, where $n\ge 1$, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur $p$-group, where $p$ is an odd prime, is isomorphic to ${\mathbb{Z}}_3\times {\mathbb{Z}}_3\times {\mathbb{Z}}_3$ or $$\mathbb{Z}$3\times $\mathbb{Z}${3^n}$,$n\geq 1$ .