关于有限群的X置换子群(英文)

On X-permutabe subgroups of finite groups

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.