december 2021 Asymptotic resemblance relations on Groups
Sh. Kalantari
Bull. Belg. Math. Soc. Simon Stevin 28(2): 217-232 (december 2021). DOI: 10.36045/j.bbms.200314

Abstract

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.

Citation

Download Citation

Sh. Kalantari. "Asymptotic resemblance relations on Groups." Bull. Belg. Math. Soc. Simon Stevin 28 (2) 217 - 232, december 2021. https://doi.org/10.36045/j.bbms.200314

Information

Published: december 2021
First available in Project Euclid: 23 December 2021

Digital Object Identifier: 10.36045/j.bbms.200314

Subjects:
Primary: 51F99 , 53C23 , 54D35 , 54F45

Keywords: asymptotic dimensiongrad , asymptotic resemblance , coarse structure , set theoretic coupling , topological coupling

Rights: Copyright © 2021 The Belgian Mathematical Society

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.28 • No. 2 • december 2021
Back to Top