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Robinson, D.J.S. (1996) A Course in the Theory of Groups. 2nd Edition, Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4419-8594-1

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• 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.