  It is shown that in the units of augmentation one of an integral group ring
$\mathbb{Z} G$ of a finite group $G$, a noncyclic subgroup of order $p^{2}$,
for some odd prime $p$, exists only if such a subgroup exists in $G$. The
corresponding statement for $p=2$ holds by the Brauer--Suzuki theorem, as
recently observed by W. Kimmerle.
