On subgroups of the general linear group containing a non-split maximal torus

Let $G=\mathrm{GL}(n,k)$ be the general linear group of degree $n$ over a field $k$ of odd characteristic. We consider subgroups of $G$ containing a non-split maximal torus stemming from a radical extension of degree $n$ of the ground field $k$. We describe the structure of nets of ideals over a ring, related to intermediate subgroups containing a transvection. Bibl. – 13 titles.