Unit groups of integral finite group rings with no noncyclic abelian finite subgroups

Abstract

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.

5 pages

References in corpus (1)

• Partial augmentations and Brauer character values of torsion units in group rings