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ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS

Year 2019, Volume: 25 Issue: 25, 35 - 42, 08.01.2019
https://doi.org/10.24330/ieja.504105

Abstract

In this paper, we study almost subnormal subgroups and maximal
subgroups in skew linear groups satisfying a generalized Laurent polynomial
identity.

References

  • S. Akbari and M. Arian-Nejad, Left Artinian algebraic algebras, Algebra Col- loq., 8(4) (2001), 463-470.
  • K. I. Beidar, W. S. Martindale 3rd and A. V. Mikhalev, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics, 196, Marcel Dekker, Inc., New York, 1996.
  • M. H. Bien, T. T. Deo and B. X. Hai, On a division subring normalized by an almost subnormal subgroup in division rings, arXiv:1801.01271.
  • M. H. Bien, D. Kiani and M. Ramezan-Nassab, Some skew linear groups sat- isfying generalized group identities, Comm. Algebra, 44(6) (2016), 2362-2367.
  • M. A. Dokuchaev and J. Z. Goncalves, Identities on units of algebraic algebras, J. Algebra, 250(2) (2002), 638-646.
  • P. K. Draxl, Skew Fields, London Mathematical Society Lecture Note Series, 81, Cambridge University Press, Cambridge, 1983.
  • B. X. Hai, T. H. Dung and M. H. Bien, Almost subnormal subgroups in division rings with generalized algebraic rational identities, arXiv:1709.04774.
  • B. Hartley, Free groups in normal subgroups of unit groups and arithmetic groups, Representation theory, group rings, and coding theory, Contemp. Math., 93, Amer. Math. Soc., Providence, RI, (1989), 173-177.
  • D. Kiani, Polynomial identities and maximal subgroups of skew linear groups, Manuscripta Math., 124(2) (2007), 269-274.
  • D. Kiani and M. Mahdavi-Hezavehi, Identities on maximal subgroups of GLn(D), Algebra Colloq., 12(3) (2005), 461-470.
  • L. Makar-Limanov, On subnormal subgroups of skew elds, J. Algebra, 114(2) (1988), 261-267.
  • N. K. Ngoc, M. H. Bien and B. X. Hai, Free subgroups in almost subnormal subgroups of general skew linear groups, St. Petersburg Math. J., 28(5) (2017), 707-717.
  • M. Ramezan-Nassab and D. Kiani, Nilpotent and polycyclic-by- nite maximal subgroups of skew linear groups, J. Algebra, 399 (2014), 269-276.
  • L. H. Rowen, Polynomial Identities in Ring Theory, Pure and Applied Mathe- matics, 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980.
Year 2019, Volume: 25 Issue: 25, 35 - 42, 08.01.2019
https://doi.org/10.24330/ieja.504105

Abstract

References

  • S. Akbari and M. Arian-Nejad, Left Artinian algebraic algebras, Algebra Col- loq., 8(4) (2001), 463-470.
  • K. I. Beidar, W. S. Martindale 3rd and A. V. Mikhalev, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics, 196, Marcel Dekker, Inc., New York, 1996.
  • M. H. Bien, T. T. Deo and B. X. Hai, On a division subring normalized by an almost subnormal subgroup in division rings, arXiv:1801.01271.
  • M. H. Bien, D. Kiani and M. Ramezan-Nassab, Some skew linear groups sat- isfying generalized group identities, Comm. Algebra, 44(6) (2016), 2362-2367.
  • M. A. Dokuchaev and J. Z. Goncalves, Identities on units of algebraic algebras, J. Algebra, 250(2) (2002), 638-646.
  • P. K. Draxl, Skew Fields, London Mathematical Society Lecture Note Series, 81, Cambridge University Press, Cambridge, 1983.
  • B. X. Hai, T. H. Dung and M. H. Bien, Almost subnormal subgroups in division rings with generalized algebraic rational identities, arXiv:1709.04774.
  • B. Hartley, Free groups in normal subgroups of unit groups and arithmetic groups, Representation theory, group rings, and coding theory, Contemp. Math., 93, Amer. Math. Soc., Providence, RI, (1989), 173-177.
  • D. Kiani, Polynomial identities and maximal subgroups of skew linear groups, Manuscripta Math., 124(2) (2007), 269-274.
  • D. Kiani and M. Mahdavi-Hezavehi, Identities on maximal subgroups of GLn(D), Algebra Colloq., 12(3) (2005), 461-470.
  • L. Makar-Limanov, On subnormal subgroups of skew elds, J. Algebra, 114(2) (1988), 261-267.
  • N. K. Ngoc, M. H. Bien and B. X. Hai, Free subgroups in almost subnormal subgroups of general skew linear groups, St. Petersburg Math. J., 28(5) (2017), 707-717.
  • M. Ramezan-Nassab and D. Kiani, Nilpotent and polycyclic-by- nite maximal subgroups of skew linear groups, J. Algebra, 399 (2014), 269-276.
  • L. H. Rowen, Polynomial Identities in Ring Theory, Pure and Applied Mathe- matics, 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Truong Huu Dung

Publication Date January 8, 2019
Published in Issue Year 2019 Volume: 25 Issue: 25

Cite

APA Dung, T. H. (2019). ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS. International Electronic Journal of Algebra, 25(25), 35-42. https://doi.org/10.24330/ieja.504105
AMA Dung TH. ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS. IEJA. January 2019;25(25):35-42. doi:10.24330/ieja.504105
Chicago Dung, Truong Huu. “ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS”. International Electronic Journal of Algebra 25, no. 25 (January 2019): 35-42. https://doi.org/10.24330/ieja.504105.
EndNote Dung TH (January 1, 2019) ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS. International Electronic Journal of Algebra 25 25 35–42.
IEEE T. H. Dung, “ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS”, IEJA, vol. 25, no. 25, pp. 35–42, 2019, doi: 10.24330/ieja.504105.
ISNAD Dung, Truong Huu. “ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS”. International Electronic Journal of Algebra 25/25 (January 2019), 35-42. https://doi.org/10.24330/ieja.504105.
JAMA Dung TH. ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS. IEJA. 2019;25:35–42.
MLA Dung, Truong Huu. “ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS”. International Electronic Journal of Algebra, vol. 25, no. 25, 2019, pp. 35-42, doi:10.24330/ieja.504105.
Vancouver Dung TH. ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS. IEJA. 2019;25(25):35-42.