有限莫利秩群的西洛2-子群的性质研究  

Study on Properties of the Sylow 2-Subgroups of Groups of Finite Morley Rank

作　　者：杨年西 

机构地区：[1]淮北师范大学信息学院

出　　处：《太原师范学院学报（自然科学版）》2017年第3期1-2,25,共3页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：安徽高校自然科学研究重点资助项目(KJ2016A646)

摘　　要：通过对有限莫利秩群的西洛2-子群探讨,分析含有2阶元素的无限群的结构,得到两个主要成果:1)一个连通的有限莫利秩的群G,且i,j∈G是两个不同的对合,假设i,j不是相互交换,如果元素阶O(i·j)=n是奇数或者O(i·j)=∞,则对合i,j在群G中是相互共轭的;2)有限莫利秩的连通群G,如果群G含有一个2-子群,则群G的西洛2-子群是无限的.We explore the Sylow 2-subgroup in groups of finite Morley rank,and analyzing On the structure of infinite groups with 2- elements. Two main conclusions are obtained. First, We show that if the product ij of two involutions i and j of a group of finite Morley rank has order ei- ther odd or infinite,then i and j are conjugate to each other. Second,we prove that let be a connected group G of finite Morley rank,and contains 2-subgroup. then the Sylow 2-subgroup of G is infinite.

关 键 词：西洛2-子群 有限莫利秩群 连通群 无限群 

分 类 号：O142[理学—数学]