This article is cited in 5 papers

Levi decomposition for carpet subgroups of Chevalley groups over a field

Ya. N. Nuzhin

Institute of Mathematics and Computer Science, Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660041 Russia

Abstract: It is proved that a carpet subgroup of a Chevalley group of type $\Phi$ over a field is a semidirect product whose kernel is defined by a unipotent carpet of type $\Phi$, while the noninvariant factor is a central product of carpet subgroups each of which is defined by an irreducible subcarpet of type $\Phi_i$ for some indecomposable root subsystem $\Phi_i$ of $\Phi$. The obtained result can be viewed as an analog of the Levi decomposition.

Keywords: Chevalley group, quasiclosed root system, carpet of additive subgroups, carpet subgroup.

UDC: 512.54

Received: 23.12.2015

DOI: 10.17377/alglog.2016.55.503

 English version: Algebra and Logic, 2016, 55:5, 367–375

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