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Main Author: Ivanov, Aleksander
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.20249
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author Ivanov, Aleksander
author_facet Ivanov, Aleksander
contents We consider metric versions of weak soficity, LEF and residual finiteness. The main results of the paper extend Glebsky and Rivera's characterization of weak soficity to the case of normally finitely generated groups with word metrics. Metric LEF and residual finiteness are also characterized in this class. We deduce that the free group $\mathsf{F}_2$ is not metrically weakly sofic with respect to its standard invariant word norm.
format Preprint
id arxiv_https___arxiv_org_abs_2410_20249
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Groups which are metrically weakly sofic with respect to word norms
Ivanov, Aleksander
Group Theory
20A15, 20E05, 20E26, 20F69
We consider metric versions of weak soficity, LEF and residual finiteness. The main results of the paper extend Glebsky and Rivera's characterization of weak soficity to the case of normally finitely generated groups with word metrics. Metric LEF and residual finiteness are also characterized in this class. We deduce that the free group $\mathsf{F}_2$ is not metrically weakly sofic with respect to its standard invariant word norm.
title Groups which are metrically weakly sofic with respect to word norms
topic Group Theory
20A15, 20E05, 20E26, 20F69
url https://arxiv.org/abs/2410.20249