CLT-Groups with Hall S-Quasinormally Embedded Subgroups

Abstract

A subgroup H of a finite group G is said to be Hall S-quasinormally embedded in G if H is a Hall subgroup of the S-quasinormal closure H ^SQG . We study finite groups G containing a Hall S-quasinormally embedded subgroup of index p ⁿ for each prime power divisor p ⁿ of the order of G.