| 雒晓良,刘合国,徐行忠,廖军.一类多重循环群的剩余有限性质[J].数学年刊A辑,2021,42(1):33~46 |
| 一类多重循环群的剩余有限性质 |
| On the Residual Finiteness of a Class of Polycyclic Groups |
| Received:November 24, 2019 Revised:August 02, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0004 |
| 中文关键词: 自由Abel群, 自同构, 多重循环群, 剩余有限群 |
| 英文关键词:Free Abelian group, Automorphism, Polycyclic group, Residually finite group |
| 基金项目:国家自然科学基金 (No.,11771129, No.,11971155, No.,12071117) |
| Author Name | Affiliation | | LUO Xiaoliang | School of Mathematics and Statistics, Hubei University, Wuhan 430062, China. | | LIU Heguo | School of Mathematics and Statistics, Hubei University, Wuhan 430062, China. | | XU Xingzhong | School of Mathematics and Statistics, Hubei University, Wuhan 430062, China. | | LIAO Jun | Corresponding author. School of Mathematics and Statistics, Hubei University,Wuhan 430062, China. |
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| 中文摘要: |
| 设A是秩为n(ngeq2)的自由Abel群, A的自同构群mathrm{Aut}(A)=mathrm{GL}(n,mathbb{Z}). 对整数m, 取begin{aligned}begin{split}alpha=begin{pmatrix} 0 & 1 & 0 & cdots & 0 0 & 0 & vdots & vdots & vdots vdots & vdots & vdots & vdots & 0 0 & 0 & cdots & 0 & 1 1 & 0 & cdots & 0 & m end{pmatrix}inmathrm{mathrm{Aut}}(A). end{split}end{aligned}记Gamma_{m}(n)=Artimeslanglealpharangle, 则它是一个2元生成的多重循环群.本文给出了Gamma_{m}(n)的准确的剩余有限性质. |
| 英文摘要: |
| Let A be a free Abelian group of rank n (ngeq2). For a rational integer m, take begin{aligned}begin{split}alpha=begin{pmatrix} 0 & 1 & 0 & cdots & 0 0 & 0 & vdots & vdots & vdots vdots & vdots & vdots & vdots & 0 0 & 0 & cdots & 0 & 1 1 & 0 & cdots & 0 & m end{pmatrix}in mathrm{Aut}(A). end{split}end{aligned}Let Gamma_{m}(n)=Artimeslanglealpharangle, then Gamma_{m}(n) is a polycyclic group generated by two elements. In this paper, the residually finiteness of Gamma_{m}(n) is analyzed.vskip 3mm |
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