中文摘要：

设H为有限群G的一个子群。称H在G中是s-半正规的，若对任意的素数p｜｜G｜，只要（p，｜H｜）=1，就有PH=HP，其中P∈Sylp（G）；称H在G中是c-可补的，若存在G的子群N，使得G=HN且H∩N≤HG=CoreG（H）。证明了下面定理 设F是一个包含超可解群类U的饱和群系，H△G，且G／H∈F。则G∈F，若下列条件之一成立：（1）若H的每个Sylow子群的所有极大子群在G中或者s-半正规或者c-可补；（2）若F^＊（H）的每个Sylow子群的所有极大子群在G中或者s-半正规或者c-可补，其中F^＊（H）是H的广义Fitting子群。该定理统一了最近的一些结果。

英文摘要：

A subgroup H of a finite group G is called s - seminormal in G if it permuts with every Sylow p - subgroup of G with（p, ｜H｜ ） = 1 ;a subgroup H of a finite group G is said to be c - supplemented in G if there exists a subgroup N of G such that and HAN≤HG = CoreG（H）. In this paper we prove following：Theorem Let F be a saturated formation containing U, the class of all supersolvable groups and G a group with a normal subgroup H such that G/ H ∈ F. Then G ∈ F if one of following holds ： （ 1 ） all maximal subgroups of any Sylow subgroup of H are either s - seminormal or c - supplemented in; （ 2 ） all maximal subgroups of all Sylow subgroups of F ^＊ （ H）, the generalized Fitting Subgroup of H,are either s -seminormal or c -supplemented in G. This unifies some recent results.