Transvections in the overgroups of a non-split maximal torus
In this paper we research intermediate subgroups of general linear group GL(n,k) of dimension n over an arbitrary field k containing non-split maximal torus associated with extension of main field k dimension n. We prove that if overgroup of non-split maximal torus contained one-dimensional transformation it would contain elementary transvections at least in two positions of any column and any row. We also prove that if extension of field k was prime overgroup of non-split maximal torus containing one-dimensional transformation would contain elementary transvections in each position.