Net determinant over a Bezoutian local ring

Let $\sigma$ be any $D$-net of ideals of order $n$ over a commutative local Bezoutian ring $R$ and denote by $G(\sigma)$ the corresponding net subgroup in the general linear group of degree $n$ over $R$ (RZhMat, 1977, 2A280). We give an explicit computation of the factor group $G(\sigma)/E(\sigma)$, where $E(\sigma)$ is the subgroup generated by all elementary transvections in $G(\sigma)$.