关于Sylow子群的极大子群的完全条件置换性

On Completely C-permutability of Maximal Subgroups of Sylow Subgroups

群G的子群H 称为G 中的完全条件置换子群,如果对G的任意子群T,存在元素x∈〈H,T〉,使HTx=TxH.利用Sylow子群的极大子群的完全条件置换性得出了下列结果:①G可解且G的每个Sylow子群的极大子群在G中完全条件置换,则G超可解;②设F是包含超可解群系U的饱和群系,N是群G 的可解的正规子群且G/N∈F,如果N的每个Sylow子群的极大子群在G中完全条件置换,则G∈F.

Subgroups H of group G is completely conditionally permutable in G if for every subgroup T of G there exists an element x∈〈H,T〉 such that HT^x=T^xH.In this paper, we give some conclusions for supersolubility of groups by using the completely c-permutability of maximal subgroups of Sylow subgroups:① Let G be a solvable group, if every maximal subgroup of Sylow subgroups of G is completely c-permutable in G, then G is supersoluble;② Let F be a saturated formation containing U.Suppose that G is group with a solvable normal subgroup N such that G/N∈F.If every maximal subgroup of Sylow subgroups of N is completely c-permutable in G, then G∈F.