Groups which are metrically weakly sofic with respect to word norms
Group Theory
2025-04-23 v2
Abstract
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 is not metrically weakly sofic with respect to its standard invariant word norm.
Cite
@article{arxiv.2410.20249,
title = {Groups which are metrically weakly sofic with respect to word norms},
author = {Aleksander Ivanov},
journal= {arXiv preprint arXiv:2410.20249},
year = {2025}
}
Comments
21 pages; small corrections in v2 (mainly in Section 3). arXiv admin note: substantial text overlap with arXiv:2311.16437