Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups

被引：0

作者：

Jun Liao

He Guo Liu

Xing Zhong Xu

Ji Ping Zhang

机构：

[1] Hubei University,Hubei Key Laboratory of Applied Mathematics, School of Mathematics and Statistics

[2] Peking University,School of Mathematical Sciences

来源：

Acta Mathematica Sinica, English Series | 2020年 / 36卷

关键词：

Nilpotent groups; central extension; isomorphic invariant; 20D15; 20E34;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1315 / 1340

页数：25