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 Z₃ × Z₃n, where n ≥ 1, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur p-group, where p is an odd prime, is isomorphic to Z₃ × Z₃ × Z₃ or Z₃ × Z₃n, n ≥ 1.