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Vladikavkaz. Mat. Zh., 2015, Volume 17, Number 4, Pages 11–17 (Mi vmj559)  

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

R. Y. Dryaevaa, V. A. Koibaevab

a 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 13-01-00469


Full text: PDF file (207 kB)
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UDC: 512.5
Received: 29.10.2014

Citation: R. Y. Dryaeva, V. A. Koibaev, “Elementary transvections in the overgroups of a non-split maximal torus”, Vladikavkaz. Mat. Zh., 17:4 (2015), 11–17

Citation in format AMSBIB
\Bibitem{DryKoi15}
\by R.~Y.~Dryaeva, V.~A.~Koibaev
\paper Elementary transvections in the overgroups of a~non-split maximal torus
\jour Vladikavkaz. Mat. Zh.
\yr 2015
\vol 17
\issue 4
\pages 11--17
\mathnet{http://mi.mathnet.ru/vmj559}


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