Absence of torsion in orbit space

Sampat Sharma

In this paper, we prove that if $R$ is a local ring of dimension $d,$ $d\geq
2$ and $\frac{1}{d!}\in R$ then the group
$\frac{Um_{d+1}(R[X])}{E_{d+1}(R[X])}$ has no $k$-torsion, provided $k\in
GL_{1}(R).$ We also prove that if $R$ is a regular ring of dimension $d,$
$d\geq 2$ and $\frac{1}{d!}\in R$ such that $E_{d+1}(R)$ acts transitively on
$Um_{d+1}(R)$ then $E_{d+1}(R[X])$ acts transitively on $Um_{d+1}(R[X]).$