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Algebra i Analiz, 2016, Volume 28, Issue 5, Pages 220–235 (Mi aa1510)  

This article is cited in 2 scientific papers (total in 2 papers)

Research Papers

Free subgroups in almost subnormal subgroups of general skew linear groups

N. K. Ngoca, M. H. Bienb, B. X. Haia

a University of Science, VNU-HCM, Faculty of Mathematics and Computer Science, 227 Nguyen Van Cu Str., Dist. 5, HCM-City, Vietnam
b Department of Basic Sciences, University of Architecture, 196 Pasteur Str., Dist. 1, HCM-City, Vietnam

Abstract: Let $D$ be a weakly locally finite division ring and $n$ a positive integer. In this paper, we investigate the problem on the existence of noncyclic free subgroups in noncentral almost subnormal subgroups of the general linear group $\mathrm{GL}_n(D)$. Further, some applications of this fact are also investigated. In particular, all infinite finitely generated almost subnormal subgroups of $\mathrm{GL}_n(D)$ are described.

Keywords: division rings, linear groups, almost subnormal subgroups, noncyclic free subgroups, generalized group identity.

Funding Agency Grant Number
Vietnam National University HoChiMinh City (VNU-HCM) B2016-18-01
This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number B2016-18-01.


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English version:
St. Petersburg Mathematical Journal, 2017, 28:5, 707–717

Bibliographic databases:

Received: 20.04.2016
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Citation: N. K. Ngoc, M. H. Bien, B. X. Hai, “Free subgroups in almost subnormal subgroups of general skew linear groups”, Algebra i Analiz, 28:5 (2016), 220–235; St. Petersburg Math. J., 28:5 (2017), 707–717

Citation in format AMSBIB
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\by N.~K.~Ngoc, M.~H.~Bien, B.~X.~Hai
\paper Free subgroups in almost subnormal subgroups of general skew linear groups
\jour Algebra i Analiz
\yr 2016
\vol 28
\issue 5
\pages 220--235
\mathnet{http://mi.mathnet.ru/aa1510}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3637590}
\transl
\jour St. Petersburg Math. J.
\yr 2017
\vol 28
\issue 5
\pages 707--717
\crossref{https://doi.org/10.1090/spmj/1468}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026286136}


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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. Truong Huu Dung, “On Almost Subnormal Subgroups and Maximal Subgroups in Skew Linear Groups”, Int. Electron. J. Algebr., 25 (2019), 35–42  crossref  mathscinet  zmath  isi  scopus
    2. Bui Xuan Hai, Huynh Viet Khanh, “Free Subgroups in Maximal Subgroups of Skew Linear Groups”, Int. J. Algebr. Comput., 29:3 (2019), 603–614  crossref  isi
  • Алгебра и анализ St. Petersburg Mathematical Journal
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