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Vladikavkaz. Mat. Zh., 2015, Volume 17, Number 2, Pages 12–15 (Mi vmj538)  

The net and elementary net group associated with non-split maximal torus

N. A. Djusoeva

North-Ossetia State University, Vladikavkaz, Russia

Abstract: The elements of matrixes of a non-split maximal torus $T=T(d)$ (associated with a radical extension $k(\sqrt[n]d)$ of degree $n$ of the ground field $k$) generate some subring $R(d)$ of the field $k$. Let $R$ be an intermediate subring, $R(d)\subseteq R\subseteq k$, $d\in R$, $A_1\subseteq…\subseteq A_n$ be a chain of ideals of the ring $R$, and $dA_n\subseteq A_1$. By $\sigma=(\sigma_{ij})$ we denote the net of ideals defined by $\sigma_{ij}=A_{i+1-j}$ with $j\leq i$ and $\sigma_{ij}=dA_{n+i+1-j}$ with $j\geq i+1$. By $G(\sigma)$ and $E(\sigma)$ we denote the net and the elementary net group, respectively. It is proved, that $TG(\sigma)$ and $TE(\sigma)$ are intermediate subgroups of $GL(n, k)$ containing the torus $T$.

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

Full text: PDF file (167 kB)
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UDC: 512.5
Received: 12.05.2015

Citation: N. A. Djusoeva, “The net and elementary net group associated with non-split maximal torus”, Vladikavkaz. Mat. Zh., 17:2 (2015), 12–15

Citation in format AMSBIB
\Bibitem{Dzh15}
\by N.~A.~Djusoeva
\paper The net and elementary net group associated with non-split maximal torus
\jour Vladikavkaz. Mat. Zh.
\yr 2015
\vol 17
\issue 2
\pages 12--15
\mathnet{http://mi.mathnet.ru/vmj538}


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