ℳ-Supplemented Subgroups and Their Properties

Abstract

A subgroup H is called ℳ-supplemented in a finite group G, if there exists a subgroup B of G such that G = HB and H ₁ B is a proper subgroup of G for any maximal subgroup H ₁ of H. In this article, we investigate the influence of ℳ-supplementation of some primary subgroups in finite groups. Some new results about supersolvable groups and formation are obtained.

Key Words:

• Finite groups
• ℳ-supplemented subgroups
• Primary subgroups
• Supersolvable groups

2000 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENTS

The authors are grateful to the referee for his/her careful reading of the manuscript and for his/her very helpful suggestions to improve our original version.

This research is supported by NSFC (10571181) and TianYuan Fund of Mathematics of China (Grant #10626047).

Notes

Communicated by M. R. Dixon.