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St. Petersburg Mathematical Journal

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Free subgroups in almost subnormal subgroups of general skew linear groups


Authors: N. K. Ngoc, M. H. Bien and B. X. Hai
Original publication: Algebra i Analiz, tom 28 (2016), nomer 5.
Journal: St. Petersburg Math. J. 28 (2017), 707-717
MSC (2010): Primary 20G15
DOI: https://doi.org/10.1090/spmj/1468
Published electronically: July 25, 2017
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Abstract: Let $ D$ be a weakly locally finite division ring and $ n$ a positive integer. The problem under study concerns the existence of noncyclic free subgroups in noncentral almost subnormal subgroups of the general linear group $ \operatorname {GL} _n(D)$. Further, some applications are also investigated. In particular, all infinite finitely generated almost subnormal subgroups of $ \operatorname {GL} _n(D)$ are described.


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Additional Information

N. K. Ngoc
Affiliation: Faculty of Mathematics and Computer Science, University of Science, VNU-HCM, 227 Nguyen Van Cu Str., Dist. 5, HCM-City, Vietnam
Email: nkngoc1985@gmail.com

M. H. Bien
Affiliation: Department of Basic Sciences, University of Architecture, 196 Pasteur Str., Dist. 1, HCM-City, Vietnam
Email: maihoangbien012@yahoo.com

B. X. Hai
Affiliation: Faculty of Mathematics and Computer Science, University of Science, VNU-HCM, 227 Nguyen Van Cu Str., Dist. 5, HCM-City, Vietnam
Email: bxhai@hcmus.edu.vn

DOI: https://doi.org/10.1090/spmj/1468
Keywords: Division rings, linear groups, almost subnormal subgroups, noncyclic free subgroups, generalized group identity
Received by editor(s): April 20, 2016
Published electronically: July 25, 2017
Additional Notes: This research was funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant no. B2016-18-01. The authors thank the referee for his/her comments
Article copyright: © Copyright 2017 American Mathematical Society

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