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.
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.