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arXiv · 0704.0412

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

Martin Hertweck
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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.

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BibTeXRIS

Martin Hertweck. 2007-04-03. Unit groups of integral finite group rings with no noncyclic abelian finite subgroups. https://arxiv.org/abs/0704.0412

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