一类无限可溶群的剩余有限性

Pub Date : 2022-03-20 DOI:10.1142/s1005386723000123

J. Liao, H. Liu, Xiaoliang Luo, Xingzhong Xu

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引用次数: 0

摘要

设[公式:见文]为秩[公式:见文]的完全可分解齐次无扭阿贝尔群([公式:见文])。设[公式:见文]是[公式:见文]通过自同构[公式:见文]的分裂扩展，该自同构[公式:见文]是由有理数整数扭曲的直接分量的循环置换[公式:见文]。则[公式:见文]是一个无限可溶群。本文研究了[公式:见文]的残差有限性。

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On the Residual Finiteness of a Class of Infinite Soluble Groups

Let [Formula: see text] be a completely decomposable homogeneous torsion-free abelian group of rank [Formula: see text] ([Formula: see text]). Let [Formula: see text] be the split extension of [Formula: see text] by an automorphism [Formula: see text] which is a cyclic permutation of the direct components twisted by a rational integer [Formula: see text]. Then [Formula: see text] is an infinite soluble group. In this paper, the residual finiteness of [Formula: see text] is investigated.

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