Bull. Korean Math. Soc. 2021; 58(1): 225-234
Online first article September 3, 2020 Printed January 31, 2021
https://doi.org/10.4134/BKMS.b200212
Copyright © The Korean Mathematical Society.
Le Qui Danh, Nguyen Trung Nghia, Nguyen Kim Ngoc
University of Architecture Ho Chi Minh City; Vietnam National University; Vietnam National University
Let $D$ be a division ring and $n>1$ be an integer. In this paper, it is shown that if $D\ne \mathbb{F}_3$, then every subpermutable subgroup of the general skew linear group ${\rm GL}_n(D)$ is normal. By applying this result, we show that every subpermutable subgroup of the unit group $(\mathbb{R} G)^*$ of the real group algebras $\mathbb{R} G$ of finite groups $G$ is normal in $(\mathbb{R} G)^*$.
Keywords: Permutable subgroup, quasinormal subgroup, subpermutable subgroup, general linear group, real group algebra
MSC numbers: 16K20, 20B99
Supported by: The third author was funded by University of Science, VNU-HCM, under grant number T2019-04
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