On σ-conditionally permutable subgroups of finite groups

AbstractLet σ be some partition of the set of all primes and H a complete Hall σ-set of a finite group G. A subgroup H of G is said to be σ-conditionally permutable in G if for any subgroup A∈H, there exists an element x∈G such that HAx=AxH. In this article, we investigate the influence of σ-conditionally permutable subgroups on the structure of finite groups.