Rendiconti del Seminario Matematico della Università di Padova
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On BNA-normality and solvability of finite groupsXuanli He, Shirong Li and Yangming Wang (1) Department of Mathematics, Guangxi University, 530004, Nanning, Guangxi, China
(2) Department of Mathematics, Guangxi University, 530004, Nanning, Guangxi, China
(3) Department of Mathematics, Sun Yat-Sen University, 510275, Guangzhou, Guangdong, China
Let $G$ be a finite group. A subgroup $H$ of $G$ is called a BNA-subgroup if either $H^x=H$ or $x\in\langle H, H^x\rangle$ for all $x\in G$. In this paper, some interesting properties of BNA-subgroups are given and, as applications, the structure of the finite groups in which all minimal subgroups are BNA-subgroups have been characterized.
Keywords: BNA-subgroup, minimal subgroup, soluble group, fitting height, $p$-length
He Xuanli, Li Shirong, Wang Yangming: On BNA-normality and solvability of finite groups. Rend. Sem. Mat. Univ. Padova 136 (2016), 51-60. doi: 10.4171/RSMUP/136-5