PM  >> Vol. 7 No. 3 (May 2017)

    有限生成无挠幂零群的有限扩张的4阶自同构
    A Finite Extension of a Finitely Generated Torsion-Free Nilpotent Groups with Automorphisms of Order Four

  • 全文下载: PDF(291KB) HTML   XML   PP.155-158   DOI: 10.12677/PM.2017.73019  
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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;
张艳萍,徐涛:河北工程大学数理学院,河北 邯郸

关键词:
有限生成无挠幂零群有限扩张自同构Finitely Generated Torsion-Free Nilpotent Group Finite Extension Automorphism

摘要:

设G是有限生成无挠幂零群的有限扩张,α是G的4阶自同构且φ: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 finite extension of a finitely generated torsion-free nilpotent group and α be an automorphism of order four of G. If the map G→G defined by Gφ=[g,α] is surjective, then the second derived subgroup G'' is included in the centre of G and CG(α2) is an Abelian group.

文章引用:
马晓迪, 张艳萍, 徐涛. 有限生成无挠幂零群的有限扩张的4阶自同构[J]. 理论数学, 2017, 7(3): 155-158. https://doi.org/10.12677/PM.2017.73019

参考文献

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[2] Burnside, W. (1955) Theory of Groups of Finite Order. 2nd Edition, Dover Publications Inc., New York.
[3] Higman, G. (1957) Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements. Journal of the London Mathematical Society, s1-32, 321-334.
https://doi.org/10.1112/jlms/s1-32.3.321
[4] Tao, X. and Liu, H.G. (2016) Finitely Generated Torsion-Free Nilpotent Groups Admitting an Automorphism of Prime Order. Communications in Mathematical Research, 32, 167-172.
[5] 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.
[6] Kovács, L.G. (1961) Group with Regular Automorphisms of Order Four. Mathematische Zeitschrift, 75, 277-294.
https://doi.org/10.1007/BF01211026