If <I>G</i> is a group of order <I>pq</i>, where<I> p</i> and <i>q</I> are prime, <i> p < q</i>, and <I>p</i> does not divide <I> q -1</I>, then <i>G </I>is cyclic.  In particular, G is isomorphic to <I> Z<sub>pq</sub>.