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http://dx.doi.org/10.4134/BKMS.b200212

SUBPERMUTABLE SUBGROUPS OF SKEW LINEAR GROUPS AND UNIT GROUPS OF REAL GROUP ALGEBRAS  

Le, Qui Danh (Department of Mathematics, Mechanics and Informatics University of Architecture Ho Chi Minh City)
Nguyen, Trung Nghia (Faculty of Mathematics and Computer Science University of Science)
Nguyen, Kim Ngoc (Faculty of Mathematics and Computer Science University of Science)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.1, 2021 , pp. 225-234 More about this Journal
Abstract
Let D be a division ring and n > 1 be an integer. In this paper, it is shown that if D ≠ ��3, then every subpermutable subgroup of the general skew linear group GLn(D) is normal. By applying this result, we show that every subpermutable subgroup of the unit group (ℝG)∗ of the real group algebras RG of finite groups G is normal in (ℝG)∗.
Keywords
Permutable subgroup; quasinormal subgroup; subpermutable subgroup; general linear group; real group algebra;
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