摘要
设X是群G的非空子集,A≤G,B≤G,若x∈X使得ABx=BxA,则称A和B在G中X-可换;若P∈Sylp(G),x∈X,使得APx=PxA,则称A在G中X-s-可换。利用有限群G的子群的X-可换及X-s-可换性刻画群G的结构,得到群G为p-超可解群的一些充分条件。
Let X be a nonempty subset of a group G.Two subgroups A and B of G are said to be X-permutable in G if there exists an element x∈X such that ABx=BxA.A subgroup A of G is said to be X-s-permutable in G if there exists an element x∈X such that APx=PxA.In this paper,X-permutable and X-s-permutable conditions are used on some subgroups of G to characterize the structure of G,and obtain some sufficient conditions for some finite group G to be p-supersolvable.
出处
《盐城工学院学报（自然科学版）》
CAS
2010年第3期21-23,共3页
Journal of Yancheng Institute of Technology:Natural Science Edition
