摘要
A subgroup H of a finite group G is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. We say that a subgroup H of a finite group G is S-semiembedded in G if there exists an s-permutable subgroup T of G such that TH is s-permutable in G and T ∩ H ≤ H-sG, where HsG is an s-semipermutable subgroup of G contained in H. In this paper, we investigate the influence of S-semiembedded subgroups on the structure of finite groups.
A subgroup H of a finite group G is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. We say that a subgroup H of a finite group G is S-semiembedded in G if there exists an s-permutable subgroup T of G such that TH is s-permutable in G and T ∩ H ≤ H-sG, where HsG is an s-semipermutable subgroup of G contained in H. In this paper, we investigate the influence of S-semiembedded subgroups on the structure of finite groups.
基金
Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11371335） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant #20113402110036）.
