On generalized m-S-permutable subgroups of a finite group

Abstract

In this paper, we give some new conditions under which a normal subgroup E of a finite group G is hypercyclically embedded in G, that is, every chief factor of G below E is cyclic.

Keywords:

• Finite group
• generalized m-S-permutable subgroup
• hypercyclically embedded subgroup
• modular subgroup
• m-S-permutable subgroup

2010 Mathematics Subject Classification:

• 20D10
• 20D15
• 20D20

Acknowledgements

The authors are very grateful to the helpful suggestions of the referee.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research is supported by an NNSF grant of China (Grant No. 11401264) and a TAPP of Jiangsu Higher Education Institutions (PPZY 2015A013)