与Sylow-子群X-可置换的子群对有限群的影响  

The Influence of Subgroups X-Permutable with Sylow Subgroups

作　　者：苏宁[1] 王燕鸣[1,2] 

机构地区：[1]中山大学数学与计算科学学院,广州510275 [2]中山大学岭南学院,广州510275

出　　处：《数学年刊（A辑）》2014年第5期511-522,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11171353);中山大学青年教师起步资助计划的资助

摘　　要：设X是有限群G中的一个非空子集,H和T是G的两个子群.称日与T在G中是X-可置换的,如果存在元素x∈X,满足HT^x=T^xH.作者探讨了当有限群G的某些子群与G的某些Sylow子群是X-可置换时G的结构.Suppose that X is a nonempty subset of a finite group G and let H and T be subgroups of G. H is said to be X-permutable with T in G if there is an element x E X such that HT^x = T^xH. This paper studies the structure of G under the assumption that certain classes of subgroups of G are X-permutable with some Sylow subgroups of G.

关 键 词：有限群 X-可置换性 P-超可解 

分 类 号：O152.1[理学—数学]