On composition factors and NS-supplemented subgroups

Abstract

In this paper, we will continue to discuss the topic on NS-supplemented subgroups proposed by Monakhov and Trofimuk. In detail, we obtained the classification of nonabelian pd-composition factors by using the NS-supplemented Sylow p-subgroup (or NS-supplemented sylowizer for every maximal subgroup of a Sylow p-subgroup) and we also investigated p-supersolvable hypercentre $Z_{p\mathcal{U}}(G)$ of a group G.

Keywords:

• pd-composition factor
• simple group
• NS-supplemented subgroup
• p-supersolvability

2020 Mathematics Subject Classification:

• 20D10
• 20D20

Acknowledgment

We would like to thank the reviewers for careful reading and their valuable comments towards improving the manuscript.

Additional information

Funding

This research is supported by the grant of NSFC (Grant # 12001436) and Chunhui Plan Cooperative Scientific Research Project of Ministry of Education of the People’s Republic of China and the Fundamental Research Funds of China West Normal University (Grant # 17E091, 18B032).