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Subpermutable subgroups of skew linear groups and unit groups of real group algebras

Le Qui Danh|Nguyen Trung Nghia|Nguyen Kim Ngoc
대한수학회 (The Korean Mathematical Society)|2021.01|대한수학회보 (Bulletin of the KMS)|제58권 제1호|pp. 225-234|DOI 10.4134/BKMS.b200212

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키워드

Permutable subgroupquasinormal subgroupsubpermutable subgroupgeneral linear groupreal group algebra
주제분류수학

초록

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 $(\mathbb{R} G)^*$.

Abstract

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 $(\mathbb{R} G)^*$.

참고문헌 (25)

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