On Schur p-Groups of odd order

摘要

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 Z(3) x Z(3)(n), 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 Z(3)x Z(3)x Z(3) or Z(3)xZ(3)(n), n >= 1.