2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126616It 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.5 pagesRepresentation TheoryRings and Algebras16S34, 16U60 (Primary) 20C05 (Secondary)text