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Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups
Acta Mathematica Sinica, English Series ( IF 0.7 ) Pub Date : 2020-12-30 , DOI: 10.1007/s10114-020-9132-8
Jun Liao , He Guo Liu , Xing Zhong Xu , Ji Ping Zhang

The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup. Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group of finite rank of infinite cyclic center, we provide a decomposition of G as the product of a generalized extraspecial ℤ-group and its center. By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial ℤ-groups, we finally obtain the structure and invariants of the group G.



中文翻译:

无限循环换向子群的有限生成幂等子群

本文的目的是确定结构,并建立无限循环换向子子群中有限生成的幂等子群G的同构不变量。利用基团的结构和不变性,该基团是无限基团的有限秩的自由阿贝尔群在循环基团的中心扩展,我们提供了G的分解,它是广义特殊ℤ基团及其中心的乘积。通过使用阿贝尔群的同构提升和广义特殊spec群的等价范式的提升技术,我们最终获得了群G的结构和不变量

更新日期:2020-12-23
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