Geodesic
Levi decomposition for carpet subgroups of Chevalley groups over a field
Algebra i logika, Tome 55 (2016) no. 5, pp. 558-570

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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. 
@article{AL_2016_55_5_a2,
     author = {Ya. N. Nuzhin},
     title = {Levi decomposition for carpet subgroups of {Chevalley} groups over a~field},
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     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_5_a2/}
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Ya. N. Nuzhin. Levi decomposition for carpet subgroups of Chevalley groups over a field. Algebra i logika, Tome 55 (2016) no. 5, pp. 558-570. http://geodesic.mathdoc.fr/item/AL_2016_55_5_a2/