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On the Residual Finiteness of a Class of Infinite Soluble Groups

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Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let Θm(n)=A×(α)be the split extension of A by an automorphismα which is a cyclic permutation of the direct components twisted by a rational integer m.Then Θm(n)is an infinite soluble group.In this paper,the residual finiteness of Θm(n)is investigated.

residual finitenessinfinite soluble groupnilpotent grouppolycyclic group

Jun Liao、Heguo Liu、Xiaoliang Luo、Xingzhong Xu

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School of Mathematics and Statistics,Hubei University,Wuhan 430062,China

Department of Mathematics,Hainan University,Haikou 570228,China

Department of Mathematics,Taiyuan Normal University Jinzhong,Shanxi 031609,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

117711291197115512071117

2023

10.1142/S1005386723000123

代数集刊(英文版)

代数集刊(英文版)

CSCD北大核心
ISSN：1005-3867
年,卷(期)：2023.30(1)
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