Author: 

Dr. M. Hertweck, Mathematisches Institut B, Universit\"at Stuttgart, 
Pfaffenwaldring 57, D-70550 Stuttgart, Germany 

Title:

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

Abstract:

Let $G$ be a finite group which has a normal $p$-subgroup $N$ with 
$\cen{G}{N}\leq N$, and let $R$ be a $p$-adic ring. Let $\NU{RG}$
denote the group of units in $RG$ of augmentation $1$. It is shown that
any finite $p$-group in $\NU{RG}$ which normalizes $N$ is conjugate to
a subgroup of $G$ in the units of $RG$, and that any finite $p$-group 
in $\NU{RG}$ which centralizes $N$ is contained in $N$.

Current status: submitted for publication