논문KCI 등재
On Engel quasi-normal subgroup in division rings with uncountable center
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The aim of this paper is to show that every Engel quasi-normal subgroups of the unit group of a division ring with uncountable center is central.
Abstract
The aim of this paper is to show that every Engel quasi-normal subgroups of the unit group of a division ring with uncountable center is central.
참고문헌 (18)
- B. Amberg, "Semilocal rings with n-Engel multiplicative group", Arch. Math. (Basel), 83(5), pp.416~421 (2004)[DOI]
- M. H. Bien, "Engel subnormal subgroups of skew linear groups", Linear Algebra Appl, 558, pp.74~78 (2018)[DOI]
- M. H. Bien, "Some algebraic algebras with Engel unit groups", J. Algebra Appl (2020)[DOI]
- A. Bovdi, "Group algebras with an Engel group of units", J. Aust. Math. Soc, 80(2), pp.173~178 (2006)[DOI]
- A. A. Bovdi, "The Engel property of the multiplicative group of a group algebra", Math. USSR-Sb, 72(1), pp.121~134 (1992)[DOI]
- L. Q. Danh, "Permutable subgroups in GLn(D) and applications to locally finite group algebras, submitted", arXiv:1912.09887, ~ (2019)
- C. Faith, "Algebraic division ring extensions", Proc. Amer. Math. Soc, 11, pp.43~53 (1960)[DOI]
- J. Z. Gon¸calves, "Free groups in subnormal subgroups and the residual nilpotence of the group of units of group rings", Canad. Math. Bull, 27(3), pp.365~370 (1984)[DOI]
- J. Z. Gon¸calves, "Construction of free subgroups in the group of units of modular group algebras", Comm. Algebra, 24(13), pp.4211~4215 (1996)[DOI]
- J. Z. Gon¸calves, "Free groups in normal subgroups of the multiplicative group of a division ring", J. Algebra, 440, pp.128~144 (2015)[DOI]
- K. W. Gruenberg, "Two theorems on Engel groups", Proc. Cambridge Philos. Soc, 49, pp.377~380 (1953)[DOI]
- L. Makar-Limanov, "Words periodic over the center of a division ring", Proc. Amer. Math. Soc, 93(4), pp.590~592 (1985)[DOI]
- M. Ramezan-Nassab, "Group algebras with Engel unit groups", J. Aust. Math. Soc, 101(2), pp.244~252 (2016)[DOI]
- M. Ramezan-Nassab, "Group algebras with locally nilpotent unit groups", Comm. Algebra, 44(2), pp.604~612 (2016)[DOI]
- M. Ramezan-Nassab, "Some skew linear groups with Engel’s condition", J. Group Theory, 15(4), pp.529~541 (2012)[DOI]
- D. M. Riley, "Group algebras with units satisfying an Engel identity", Rend. Circ. Mat. Palermo (2), 49(3), pp.540~544 (2000)[DOI]
- L. H. Rowen, "Polynomial identities in ring theory" (1980), Academic Press, Inc.
- D. A. Suprunenko, "Linear groups with Engel’s condition", Dokl. Akad. Nauk BSSR, 6, pp.277~280 (1962)
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