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DOI: 10.23671/VNC.2014.3.10228

Transvection modules in the overgroups of a non-split maximal torus

Koibaev, V. A. , Dzhusoeva, N. A.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 3.
The aim of this article is to investigate the modules of transvections  and rings of multipliers subgroups of the general linear group \(G=GL(n,k)\) of degree \(n\) over a field \(k\), containing non-split maximal torus \(T=T(d)\), associated with a radical extension of \(k(\sqrt[n]{d})\) of the degree \(n\) of the
ground field \(k\) of an odd characteristic (minisotropic torus). We find a full list  of \(2\cdot[(\frac{n-1}{2})^{2}]\) relations (\([\cdot]\) -
integer part) of the modules of transvections. We prove that all ring of multipliers coincide,  and all modules  transvections are ideals of the ring of multipliers. All results were proved by the assumption that the ground field \(k\) is the field of fractions of a principal ideal domain.
Keywords: overgroups, intermediate subgroups, non-split maximal torus, transvection, module transvections
Language: Russian Download the full text  
For citation: Koibaev V. A., Dzhusoeva N. A. Transvection modules in the overgroups of a non-split maximal torus // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 3, pp. 3-8. DOI 10.23671/VNC.2014.3.10228
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