群上的渐近相似关系

IF 0.4 4区数学 Q4 MATHEMATICS Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2021-11-10 DOI:10.36045/j.bbms.200314

Sh. Kalantari

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引用次数: 0

摘要

本文研究了群上相容粗结构引起的渐近相似关系的性质。推广了具有相容粗结构群的渐近维梯度的概念，并证明了这一概念是粗不变的。最后，我们定义了相容粗糙结构群的集合论耦合概念，并证明了这一概念是有限生成群的拓扑耦合概念的推广。我们证明了如果两个相容粗结构群允许集论耦合，那么它们是渐近等价的。

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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Asymptotic resemblance relations on Groups

In this paper, we study properties of asymptotic resemblance relations induced by compatible coarse structures on groups. We generalize the notion of asymptotic dimensiongrad for groups with compatible coarse structures and show this notion is coarse invariant. We end by defining the notion of set theoretic coupling for groups with compatible coarse structures and showing this notion is the generalization of the notion of topological coupling for finitely generated groups. We show if two groups with compatible coarse structures admit a set theoretic coupling then they are asymptotic equivalent.

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来源期刊

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.

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