This article is cited in 6 papers

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

V. A. Koibaev^ab, Ya. N. Nuzhin<sup>c

a</sup> 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.

UDC: 512.5

MSC: 35R30

Received: 16.01.2016

DOI: 10.17377/smzh.2017.58.114

 English version: Siberian Mathematical Journal, 2017, 58:1, 109–112

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