On a maximal torus in subgroups of a general linear group (Q1376901)

Given a finite field extension \(K/k\) of degree \(n\), one can use the regular representation and construct an algebraic torus \(T\) of dimension \(n\) which can be viewed as a maximal (non-split) torus in \(G=\text{GL}(n,k)\). If \(G'\) is a subgroup of \(G\), the authors are interested whether \(T'=T\cap G'\) is a maximal torus in \(G'\). They formulate some sufficient conditions and check them for certain classical groups \(G'\).