On maximal subgroups of the general linear group over rational functions field

N. A. Dzhusoeva^a, V. S. Dzigoeva^a, V. A. Koibaev<sup>ab

a</sup> North-Ossetia State University, Russia, Vladikavkaz
^b Southern Federal University, Russia, Vladikavkaz

Abstract: We construct a class of the maximal subgroups of the general linear group $G=\mathrm{GL}(n,k(x))$ of degree $n$ over a field of the rational functions $k(x)$ with coefficients in a field $k$ of odd characteristic, containing non-split maximal torus associated with the radical extension of the basic field $k(x)$.

Key words: intermediate subgroups, maximal subgroups, non-split maximal torus, transvection.

UDC: 519.46

Received: 14.10.2010