An irrational-slope Thompson’s group

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2018-05-31 DOI:10.5565/PUBLMAT6522112

J. Burillo, Brita Nucinkis, Lawrence Reeves

引用次数: 14

Abstract

The purpose of this paper is to study the properties of the irrational-slope Thompson's group $F_\tau$ introduced by Cleary in 1995. We construct presentations, both finite and infinite and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of $F$ in $F_\tau$ are undistorted.

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一个非理性斜率汤普森组

本文的目的是研究Cleary(1995)引入的非理性斜率汤普森群的性质。我们构造有限和无限的表示，并使用二叉树描述其组合结构。证明了它的换向子群是简单的。最后，受Thompson群F的启发，我们定义了群中元素的唯一范式，并在此范式的基础上研究了元素的度量性质。作为推论，我们看到$F$的几个嵌入$F_\tau$是未失真的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.