Generalized Residual Finiteness of Groups
Group Theory
2024-01-11 v2
Abstract
A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many conjugacy classes of elements fail to act nontrivially on a finite set, or it could be that the group has no nontrivial actions on finite sets whatsoever. We define a hierarchy of properties, and construct groups which become arbitrarily complicated in this sense.
Keywords
Cite
@article{arxiv.2312.15120,
title = {Generalized Residual Finiteness of Groups},
author = {Nic Brody and Kasia Jankiewicz},
journal= {arXiv preprint arXiv:2312.15120},
year = {2024}
}
Comments
8 pages. Comments are welcome! v2: Added references, corrected errors