In this paper, we prove that if [Formula: see text] is a local ring of dimension [Formula: see text] [Formula: see text] and [Formula: see text] then the group [Formula: see text] has no [Formula: see text]-torsion, provided [Formula: see text] We also prove that if [Formula: see text] is a regular ring of dimension [Formula: see text] [Formula: see text] and [Formula: see text] such that [Formula: see text] acts transitively on [Formula: see text] then [Formula: see text] acts transitively on [Formula: see text]
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