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Algebra Logika, 2016, Volume 55, Number 5, Pages 558–570 (Mi al761)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00707
Supported by RFBR, project No. 16-01-00707.


DOI: https://doi.org/10.17377/alglog.2016.55.503

Full text: PDF file (160 kB)
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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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\paper Levi decomposition for carpet subgroups of Chevalley groups over a~field
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\vol 55
\issue 5
\pages 558--570
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\jour Algebra and Logic
\yr 2016
\vol 55
\issue 5
\pages 367--375
\crossref{https://doi.org/10.1007/s10469-016-9408-3}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. K. Franchuk, “O neprivodimykh kovrakh additivnykh podgrupp tipa $G_2$”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 80–86  mathnet  crossref
    2. 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  mathnet
    3. S. K. Franchuk, “O neprivodimykh kovrakh additivnykh podgrupp tipa $G_2$ nad polyami kharakteristiki $p>0$”, Vladikavk. matem. zhurn., 22:1 (2020), 78–84  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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