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
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。
Abstract:
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.
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