The net and elementary net group associated with non-split maximal torus

The elements of matrixes of a non-split maximal torus $T=T(d)$ (associated with a radical extension $k(\sqrt[n]{d})$ of degree $n$ of the ground field $k$) generate some subring $R(d)$ of the field $k$. Let $R$ be an intermediate subring, $R(d)\subseteq{R}\subseteq{k}$, $d\in{R}$, $A_1\subseteq\dots\subseteq A_n$ be a chain of ideals of the ring $R$, and $ d A_n\subseteq A_1.$ By $\sigma = (\sigma_{ij})$ we denote the net of ideals defined by $\sigma_{ij}= A_{i+1-j}$ with $ j\leq i$ and $\sigma_{ij}=dA_{n+i+1-j}$ with $j\geq i+1$. By $G(\sigma)$ and $E(\sigma)$ we denote the net and the elementary net group, respectively. It is proved, that $TG(\sigma)$ and $TE(\sigma)$ are intermediate subgroups of $GL(n, k)$ containing the torus $T$.