有限群超可解性的一个新刻画  

A new characterization of supersolubility of finite groups

作　　者：唐娜[1,2] 黎先华[2] 

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223300 [2]苏州大学数学科学学院,江苏苏州215006

出　　处：《扬州大学学报（自然科学版）》2013年第3期1-3,共3页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11171243);国家自然科学基金天元基金资助项目(11226285)

摘　　要：若存在x∈〈H,T〉,有HTx=Tx H,则子群H和T在群G中完全条件置换.利用完全条件置换子群,给出了群G的超可解性的刻画:可解群G超可解的充分必要条件是存在G的正规子群N满足G/N超可解,且N的每个Sylow子群的极大子群与G的所有Hall子群完全条件置换.The subgroups H and T are said to be completely conditionally permutable in G if for some x ∈（H, T） there exists HTT ^x= T^xH. In this paper, taking advantage of some completely conditionally permutable subgroup, the characterization of the supersolubility of group G is given： A solvable group G is supersolvable if and only if there exists a normal subgroup N such that G/N is supersolvable and every maximal subgroup of any Sylow subgroups of N is completely conditionally permutable with every Hall subgroup of G.

关 键 词：完全条件置换子群 超可解 HALL子群 极大子群 

分 类 号：O152.1[理学—数学]