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

Abstract

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 $N$.

12 pages

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