S-条件置换子群对有限群结构的影响

The Influence of S-conditionally Permutable Subgroups on the Structure of Finite Group

利用子群的S-条件置换性,得到了有限超可解群的一充分条件;并得到有限群G∈F的一充分必要条件.即:设F是一个包含所有超可解群类U的饱和群系.则有限群G∈F,当且仅当G有一个正规子群H,使得G/H∈F且F*(H)∩G的GP极大子群在G中S-条件置换.其中GP是G的非循环Sylow子群.

A sufficient condition of finite supersovlable groups is obtained by using the s-conditionally permutable subgroups ; And a sufficient and necessary condition of finite group G ∈ F is got. i.e. Let F be a saturated formation containing U. Then G∈ F if and only if G is a group with a normal subgroup such that G/H ∈ F and all maximal subgroups of F^＊ （H）∩ Gp axe s-conditionally permutable in G . Where Gp is a noncyele Slyow subgroup of G .