SUBGROUPS OF THE MULTIPLICATIVE GROUP OF THE DIVISION RING OF REAL QUATERNIONS
Main Article Content
Abstract
Let be the division ring of real quaternions and the multiplicative group of A subgroup of is said to be almost subnormal if a sequence of subgroups exists
such that for any is normal in or has the finite index in In this paper, we show that every almost subnormal subgroup of is normal.
Keywords
division ring, division ring of real quaternions, almost subnormal subgroup
Article Details
References
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Tomanov, G. M. (1985). Generalized group identities in linear groups. Math. USSR, Sbornik, 51,
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Wehfritz, B. A. F. (1993). A note on almost subnormal subgroups of linear groups. Proc. Am. Math. Soc, 117(1), 17-21.
Greenfield, G. R. (1978). A note on subnormal subgroups of division algebras. Can. J. Math, 30, 161-163.
Hartley, B. (1989). Free groups in normal subgroups of unit groups and arithmetic groups. Contemp. Math, 93, 173-177.
Hazrat, R., & Wadsworth, A. R. (2009). On maximal subgroups of the multiplicative group of a division algebra. J. Algebra, 322, 2528-2543.
Lam, T. Y. (1991). A first course in noncommutative rings. Berlin. Springer-Vetlag.
Mai, H. B. (2015). On some subgroups of which satisfy a generalized group identity. Bull. Korean Math. Soc., 52, 1353-1363.
Nguyen, K. N., Mai, H. B., & Bui, X. H. (2017). Free subgroups in almost subnormal subgroups of general skew linear groups. Algebra i Analiz, 28(5), 220-235, English translation in St. Petersburg Math. J., 28(5), 707-717.
Trinh, T. D., Mai, H. B., & Bui. X. H. (2019). On division subrings normalized by almost subnormal subgroups in division rings. Periodica Mathematica Hungarica.
Tomanov, G. M. (1985). Generalized group identities in linear groups. Math. USSR, Sbornik, 51,
33-46.
Wehfritz, B. A. F. (1993). A note on almost subnormal subgroups of linear groups. Proc. Am. Math. Soc, 117(1), 17-21.