Geodesic
Elementary transvections in the overgroups of a~non-split maximal torus
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 4, pp. 11-17

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A subgroup $H$ of the general linear group $GL(n,k)$ is rich in transvections if $H$ contains elementary transvections $t_{ij}(\alpha)$ at all positions $(i,j)$, $i\neq j$. In this paper we show that if a subgroup $H$ contains a non-split maximal torus and elementary transvection in one position, than $H$ is rich in transvections. It is also proved that if a subgroup $H$ contains a cyclic permutation of order $n$ and elementary transvection at position $(i,j)$ such that numbers $i-j$ and $n$ are coprime, then $H$ is rich in transvections. 
@article{VMJ_2015_17_4_a1,
     author = {R. Y. Dryaeva and V. A. Koibaev},
     title = {Elementary transvections in the overgroups of a~non-split maximal torus},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {11--17},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2015_17_4_a1/}
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R. Y. Dryaeva; V. A. Koibaev. Elementary transvections in the overgroups of a~non-split maximal torus. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 4, pp. 11-17. http://geodesic.mathdoc.fr/item/VMJ_2015_17_4_a1/