# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 136, 2016, pp. 51–60**

**DOI: 10.4171/RSMUP/136-5**

On BNA-normality and solvability of finite groups

Xuanli He^{[1]}, Shirong Li

^{[2]}and Yangming Wang

^{[3]}(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