Free subgroups in almost subnormal subgroups of general skew linear groups
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- by N. K. Ngoc, M. H. Bien and B. X. Hai
- St. Petersburg Math. J. 28 (2017), 707-717
- 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.References
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Bibliographic 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
- 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
- © Copyright 2017 American Mathematical Society
- Journal: St. Petersburg Math. J. 28 (2017), 707-717
- MSC (2010): Primary 20G15
- DOI: https://doi.org/10.1090/spmj/1468
- MathSciNet review: 3637590