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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 143–147 (Mi smj2847)  

This article is cited in 1 scientific paper (total in 1 paper)

$k$-invariant nets over an algebraic extension of a field $k$

V. A. Koibaevab, Ya. N. Nuzhinc

a North Ossetian State University named after K. L. Hetagurov, Vladikavkaz, Russia
b Southern Mathematical Institute, Vladikavkaz, Russia
c Siberian Federal University, Krasnoyarsk, Russia

Abstract: Let $K$ be an algebraic extension of a field $k$, let $\sigma=(\sigma_{ij})$ be an irreducible full (elementary) net of order $n\geq2$ (respectively, $n\geq3$) over $K$, while the additive subgroups $\sigma_{ij}$ are $k$-subspaces of $K$. We prove that all $\sigma_{ij}$ coincide with an intermediate subfield $P$, $k\subseteq P\subseteq K$, up to conjugation by a diagonal matrix.

Keywords: general and special linear groups, full and elementary nets of additive subgroups, net subgroup, algebraic extension of a field.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 115033020013
Russian Foundation for Basic Research 16-01-00707
The first author was supported by the Ministry of Education and Science of the Russian Federation under Open Research and Development Program 115033020013. The second author was supported by the Russian Foundation for Basic Research (Grant 16-01-00707).


DOI: https://doi.org/10.17377/smzh.2017.58.114

Full text: PDF file (253 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:1, 109–112

Bibliographic databases:

UDC: 512.5
MSC: 35R30
Received: 16.01.2016

Citation: V. A. Koibaev, Ya. N. Nuzhin, “$k$-invariant nets over an algebraic extension of a field $k$”, Sibirsk. Mat. Zh., 58:1 (2017), 143–147; Siberian Math. J., 58:1 (2017), 109–112

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. S. K. Franchuk, “O neprivodimykh kovrakh additivnykh podgrupp tipa $G_2$”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 80–86  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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