2019
Том 71
№ 11

All Issues

Li S.

Articles: 1
Brief Communications (English)

Groups all cyclic subgroups of which are BN A-subgroups

He X., Li S., Wang Youyu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 284-288

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is a BN A-subgroup of $G$ if either $H^x = H$ or $x \in \langle H, H^x\rangle$ for all $x \in G$. The BN A-subgroups of $G$ are between normal and abnormal subgroups of $G$. We obtain some new characterizations for finite groups based on the assumption that all cyclic subgroups are BN A-subgroups.