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

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     journal = {Algebra i logika},
     pages = {558--570},
     publisher = {mathdoc},
     volume = {55},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_5_a2/}
}
TY  - JOUR
AU  - Ya. N. Nuzhin
TI  - Levi decomposition for carpet subgroups of Chevalley groups over a~field
JO  - Algebra i logika
PY  - 2016
SP  - 558
EP  - 570
VL  - 55
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2016_55_5_a2/
LA  - ru
ID  - AL_2016_55_5_a2
ER  - 
%0 Journal Article
%A Ya. N. Nuzhin
%T Levi decomposition for carpet subgroups of Chevalley groups over a~field
%J Algebra i logika
%D 2016
%P 558-570
%V 55
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2016_55_5_a2/
%G ru
%F AL_2016_55_5_a2
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/

[1] Ya. N. Nuzhin, “Faktorizatsiya kovrovykh podgrupp grupp Shevalle nad kommutativnymi koltsami”, Zhurn. SFU. Ser. Matem. i fiz., 4:4 (2011), 527–535

[2] R. Steinberg, Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR

[3] R. W. Carter, Simple groups of Lie type, Pure and Appl. Math., 28, John Wiley Sons, A Wiley Interscience Publication, London a.o., 1972 | MR

[4] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980

[5] A. Borel, J. Tits, “Groupes réductifs”, Publ. Math. Inst. Hautes Étud. Sci., 27 (1965), 659–755 ; A. Borel, Zh. Tits, “Reduktivnye gruppy”, Sb. Matematika, 11:1 (1983), 43–111; Sb. Matematika, 11:2 (1983), 3–31 | MR | Zbl

[6] V. M. Levchuk, “O porozhdayuschikh mnozhestvakh kornevykh elementov grupp Shevalle nad polem”, Algebra i logika, 22:5 (1983), 504–517 | MR | Zbl