Abstract
Let d be the smallest generator number of a finite p-group P, and let ℳ
d
(P) = {P
1, P
2,…, P
d
} be a set of maximal subgroups of P such that . Then P is called ℳ-permutable in a finite group G, if there exists a subgroup B of G such that G = PB and P
i
B < G for any P
i
of ℳ
d
(P). In this article, we investigate the influence of ℳ-permutability of some primary subgroups in finite groups. Some new results about supersolvable groups and formations are obtained.
ACKNOWLEDGMENTS
Authors are grateful for the referee for his/her helpful comments.
The first author is supported by the grant of NSFC (Grant #10901133) and sponsored by Qing Lan Project and Natural Science Fund for colleges and universities in Jiangsu Province.
Notes
Communicated by V. A. Artamonov.