This article is cited in 2 papers

Elementary transvections in the overgroups of a non-split maximal torus

R. Y. Dryaeva^a, V. A. Koibaev<sup>ab

a</sup> North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia
^b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia

Abstract: 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.

Key words: overgroup, intermediate subgroup, non-split maximal torus, transvection, elementary transvection.

UDC: 512.5

Received: 29.10.2014