The net and elementary net group associated with non-split maximal torus
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 2, pp. 12-15
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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, $R(d)\subseteq R\subseteq k$, $d\in R$, $A_1\subseteq\dots\subseteq A_n$ 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 $T$.
@article{VMJ_2015_17_2_a1,
author = {N. A. Djusoeva},
title = {The net and elementary net group associated with non-split maximal torus},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {12--15},
year = {2015},
volume = {17},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a1/}
}
N. A. Djusoeva. The net and elementary net group associated with non-split maximal torus. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 2, pp. 12-15. http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a1/
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