Units of $p$-power order in principal $p$-blocks of $p$-constrained groups

Details Units of $p$-power order in principal $p$-blocks of $p$-constrained groups Units of $p$-power order in principal $p$-blocks of $p$-constrained groups

2006-12-15

arxiv.org/abs/math/0612434v1

Mathematics

Representation Theory

12 pages

Scientific paper

Let $G$ be a finite group having a normal $p$-subgroup $N$ that contains its
centralizer $\text{C}_{G}(N)$, and let $R$ be a $p$-adic ring. It is shown that
any finite $p$-group of units of augmentation one in $RG$ which normalizes $N$
is conjugate to a subgroup of $G$ by a unit of $RG$, and if it centralizes $N$
it is even contained in $N$.

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