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

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

2007-04-03

arxiv.org/abs/0704.0412v1

Mathematics

Representation Theory

5 pages

Scientific paper

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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