Abstract
We call a subgroup H of a group G nearly s-normal in G if there exists N ⊴ G such that HN ⊴ G and H ∩ N ≤ H sG , where H sG is the largest s-permutable subgroup of G contained in H. In this article, we obtain some results about the nearly s-normal subgroups and use them to characterize the structure of finite groups.
ACKNOWLEDGMENT
Research is supported by NNSF of China (Grant #11071229) and by Postgraduate Key Fund of Xuzhou Normal University.
Notes
Communicated by V. A. Artamonov.