The influence of s-conditionally permutable subgroups on finite groups

A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HT ^x = T ^x H. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting results are generalized. This work was supported by National Natural Science Foundation of China (Grant No. 10771180), Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 08zb059) and Research Programme of Chengdu University of Information Technology