Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups

被引：0

作者：

Jun LIAO ^{[1
]}

He Guo LIU ^{[1
]}

Xing Zhong XU ^{[1
]}

Ji Ping ZHANG ^{[2
]}

机构：

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

[2] School of Mathematical Sciences, Peking University

来源：

Acta Mathematica Sinica,English Series | 2020年 / 12期

关键词：

D O I：

暂无

中图分类号：

O152 [群论];

学科分类号：

070104 ;

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 offinite 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：26