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 :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 GG 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 (2016) 有限生成无挠幂零群的4阶自同构。 理论数学, 6, 437-440. doi: 10.12677/PM.2016.65059

参考文献

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