Connecting the space of marked groups and the space of group operations
Logic
2025-10-22 v2 Group Theory
Abstract
We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the sense of Baire category, which allows us to translate several results from the former setting to the latter. As an application, we give new, shorter proofs of two theorems that concern the generic behavior of compact metrizable abelian groups.
Cite
@article{arxiv.2503.14638,
title = {Connecting the space of marked groups and the space of group operations},
author = {Tamás Kátay},
journal= {arXiv preprint arXiv:2503.14638},
year = {2025}
}
Comments
14 pages, 1 figure. Appendix added