标题:
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
作者:
马晓迪, 徐涛
关键字:
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
期刊名称:
《Pure Mathematics》, Vol.6 No.5, 2016-09-26
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。
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.