ON ALMOST SUBNORMAL SUBGROUPS AND MAXIMAL SUBGROUPS IN SKEW LINEAR GROUPS

Year 2019, Volume: 25 Issue: 25, 35 - 42, 08.01.2019

Truong Huu Dung

https://doi.org/10.24330/ieja.504105

https://izlik.org/JA98MC65DL

Abstract

In this paper, we study almost subnormal subgroups and maximal

subgroups in skew linear groups satisfying a generalized Laurent polynomial

identity.

Keywords

Division ring , linear group , almost subnormal subgroup , maximal subgroup , 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.