摘要
令A,B是一个群G的两个子群,X是G的一个非空子集,称A与B是X可置换的,如果存在X中的一个元x,使得ABx=BxA.对X置换子群和它们的一些应用进行了综合评述,介绍了一系列相关的重要成果和一些未解决的问题.
Let A, B be subgroups of a group G and X a non-empty subset of G. Then we say that A is X-permutable with B if there exists some x∈ X such that AB^x =B^xA. The purpose of the paper is to give a review about X-permutable subgroups and some their applications. A series of related important results and questions are introduced.
出处
《徐州师范大学学报（自然科学版）》
CAS
2009年第2期16-24,共9页
Journal of Xuzhou Normal University(Natural Science Edition)
基金
supported by the National Natural Science Foundation of China(10771180)
关键词
有限群
置换子群
条件置换子群
完全条件置换子群
X置换子群
S条件置换子群
X-s置换子群
可解群
超可解群
幂零群
饱和群系
HALL子群
极大子群
finite group
permutable subgroup
conditionally permutable subgroup
completely c-permutable subgroup
X-permutable subgroup
S-conditionally permutable subgroup
X-s-permutable subgroup
soluble group
supersoluble group
nilpotent group
saturated formation
Hall subgroup
maximal subgroup
