Descriptive complexity of subsets of the space of finitely generated groups

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2022-12-01 DOI:10.1016/j.exmath.2022.08.001

Mustafa Gökhan Benli̇, Burak Kaya

引用次数: 3

Abstract

In this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups, groups of exponential growth and groups with decidable word problem are $Σ_{2}^{0}$ -complete and that the sets of periodic groups and groups of intermediate growth are $Π_{2}^{0}$ -complete. We also provide bounds for the descriptive complexity of simplicity, amenability, residually finiteness, Hopficity and co-Hopficity. This paper is intended to serve as a compilation of results on this theme.

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有限生成群空间子集的描述复杂度

本文确定了由各种群论性质所定义的标记群的波兰空间的子集的描述复杂度。特别地，利用Grigorchuk群，我们建立了可解群、指数增长群和可决字问题群的集合为Σ20-complete，周期群和中间增长群的集合为Π20-complete。我们还给出了简单性、适应性、剩余有限性、合性和共合性的描述复杂性的界。本文旨在汇编关于这一主题的研究结果。

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

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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