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This article is cited in 3 scientific papers (total in 3 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.
DOI:
https://doi.org/10.17377/alglog.2016.55.503
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English version:
Algebra and Logic, 2016, 55:5, 367–375
Bibliographic databases:
 
UDC:
512.54
Received: 23.12.2015
Citation:
Ya. N. Nuzhin, “Levi decomposition for carpet subgroups of Chevalley groups over a field”, Algebra Logika, 55:5 (2016), 558–570; Algebra and Logic, 55:5 (2016), 367–375
Citation in format AMSBIB
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\pages 558--570
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Linking options:
http://mi.mathnet.ru/eng/al761 http://mi.mathnet.ru/eng/al/v55/i5/p558
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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S. K. Franchuk, “O neprivodimykh kovrakh additivnykh podgrupp tipa $G_2$”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 80–86
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Ya. N. Nuzhin, A. V. Stepanov, “Podgruppy grupp Shevalle tipov $B_l$ i $C_l$, soderzhaschie gruppu nad podkoltsom, i svyazannye s nimi kovry”, Algebra i analiz, 31:4 (2019), 198–224
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S. K. Franchuk, “O neprivodimykh kovrakh additivnykh podgrupp tipa $G_2$ nad polyami kharakteristiki $p>0$”, Vladikavk. matem. zhurn., 22:1 (2020), 78–84
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