On P-F-Supplemented subgroups of finite groups

摘要

Let F be a class of groups and G a finite group. A maximal subgroup M of G is called F-abnormal provided G/M-G is not an element of F a. Let K < H be subgroup of G. Then we say that (I(,H) is an F-abnormal pair of G provided K is a maximal F-abnormal subgroup of H. Let A be a subgroup, of G. Then we say that A is F-quasipermutable in G provided A either covers or avoids every F-abnormal pair of G. In this paper, we consider some applications of F-quasipermutable subgroups.