有限生成无挠幂零群的4阶自同构
Finitely Generated Torsion-Free Nilpotent Groups Admitting an Automorphism of Order Four
DOI: 10.12677/PM.2016.65059, PDF, HTML, XML, 下载: 1,776  浏览: 3,112  科研立项经费支持
作者: 马 晓迪：南京理工大学计算机科学与工程学院，江苏 南京；徐 涛：河北工程大学理学院，河北 邯郸
关键词: 有限生成；无挠幂零群；正则自同构；自同构；Finitely Generated； Torsion-Free Nilpotent Group； Regular Automorphism； Automorphism
摘要: 设G是有限生成无挠幂零群，α是G的4阶自同构且 是满射，则G的二阶导群G'' 包含在G的中心Z(G) 里且CG(α2) 是Abel群。
Abstract: Let G be a finitely generated torsion-free nilpotent group and α an automorphism of order four of G. If the map G→G defined by is surjective, then the second derived subgroup G'' is included in the centre of G and CG(α2) is abelian.
文章引用：马晓迪, 徐涛. 有限生成无挠幂零群的4阶自同构[J]. 理论数学, 2016, 6(5): 437-440. http://dx.doi.org/10.12677/PM.2016.65059

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