Complexity among the finitely generated subgroups of Thompson's group

Bleak Collin; Brin Matthew G.; Moore Justin Tatch

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Complexity among the finitely generated subgroups of Thompson's group

机译：复杂性有限生成的子组汤普森的组

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We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson's group F which is strictly well-ordered by the embeddability relation of type epsilon(0)+Sigma 1. All except the maximum element of this family (which is F itself) are elementary amenable groups. In fact we also obtain, for each alpha < epsilon(0), a finitely generated elementary amenable subgroup of F whose EA-class is alpha + 2. These groups all have simple, explicit descriptions and can be viewed as a natural continuation of the progression which starts with Z + Z, Z (sic) Z, and the Brin-Navas group B. We also give an example of a pair of finitely generated elementary amenable subgroups of F with the property that neither is embeddable into the other.

机译：我们将演示一个家庭的存在理查德的有限生成子组汤普森的F组严格秩序井然的关系嵌入性的类型ε(0)+σ1。这个家庭的元素(F)基本的组。获得,对于每个α<ε(0),一个有限生成基本的子群的FEA-class是α+ 2。简单、明确的描述,可以查看作为一个自然的延续发展开始与Z + Z Z Z(原文如此),和Brin-Navas集团给出的一个例子一双有限生成基本的子也不是F的属性可嵌入到另一个。

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《Journal of combinatorial algebra》 |2021年第1期|1-58|共58页
作者
Bleak Collin; Brin Matthew G.; Moore Justin Tatch;
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作者单位

Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA;

SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA;

Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland;

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正文语种英语
中图分类
关键词
Complexity; Ordinal; Elementaryfamily;

机译：复杂性;序数;Elementaryfamily;

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Complexity among the finitely generated subgroups of Thompson's group

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