Subpermutable subgroups of skew linear groups and unit groups of real group algebras
Bull. Korean Math. Soc.
Published online September 3, 2020
Le Qui Danh, Nguyen Trung Nghia, and Nguyen Kim Ngoc
University of Architecture Ho Chi Minh City, Faculty of Mathematics and Computer Science, University of Science, Ho Chi MinhCity, Vietnam; Vietnam National University, Ho Chi Minh City, Vietnam
Abstract : Let $D$ be a division ring and $n>1$. In this paper, it is shown that if $D\ne \mathbb{F}_3$, then every subpermutable subgroup of the skew general linear group $\text{GL}_n(D)$ is normal. By applying this result, we show that every subpermutable subgroup of the unit group $(\mathbb{R} G)^*$ of the real group algebra $\mathbb{R} G$ 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
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