On S_*-embedded subgroups of finite groups

Abstract

We introduce a new subgroup embedding property, namely $S_{*}$-embedded subgroup and study the structure of a finite group G under the assumption that some subgroups of prime order are $S_{*}$-embedded in G. A serie of known results are unified and extended.

Keywords:

• S_*-embedded
• S-permutable
• S-permutably embedded
• Sylow subgroups

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Additional information

Funding

The project is supported by the Natural Science Foundation of China (Nos. 11401264 and 11571145) and the Natural Science Research Project of Universities in Anhui Province (KJ2019A0142).