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.
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有限生成无挠幂零群的有限扩张的4阶自同构
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A Finite Extension of a Finitely Generated Torsion-Free Nilpotent Groups with Automorphisms of Order Four[J]. 理论数学, 2017, 07(03): 155-158. http://dx.doi.org/10.12677/PM.2017.73019
参考文献 (References)ReferencesRobinson, D.J.S. (1996) A Course in the Theory of Groups. 2nd Edition, Springer-Verlag, New York.
<br>https://doi.org/10.1007/978-1-4419-8594-1Burnside, W. (1955) Theory of Groups of Finite Order. 2nd Edition, Dover Publications Inc., New York.Higman, G. (1957) Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements. Journal of the London Mathematical Society, s1-32, 321-334. <br>https://doi.org/10.1112/jlms/s1-32.3.321Tao, 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.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.Kovács, L.G. (1961) Group with Regular Automorphisms of Order Four. Mathematische Zeitschrift, 75, 277-294.
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