On weakly BNA-subgroups of finite groups

Abstract

Let G be a finite group. A subgroup H of G is called a BNA-subgroup of G if either $H^x=H$ or $x\in 〈H,H^x〉$ for all $x\in G.$ A subgroup H of G is said to be a weakly BNA-subgroup of G if there exists a normal subgroup T of G such that G = HT and $H\cap T$ is a BNA-subgroup of G. In this paper, we investigate the solvability, supersolvability, and p-nilpotency of a finite group G under the assumption that certain minimal subgroups and cyclic subgroups of order 4 are weakly BNA-subgroups of G.

Keywords:

• p-Nilpotency
• solvability
• supersolvability
• weakly BNA-subgroup

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20D10
• 20D20

Additional information

Funding

This research was supported by NSFC (No. 12071484), Hunan Provincial Natural Science Foundation (2020JJ4675) and Guangxi Natural Science Foundation Program (2021GXNSFAA220105). The authors are very grateful to the referee for her/his valuable suggestions and useful comments.