Generalized Residual Finiteness of Groups

Fuente: arXiv
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Main Authors: Brody, Nic, Jankiewicz, Kasia
Format: Preprint
Published: 2023
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author Brody, Nic
Jankiewicz, Kasia
author_facet Brody, Nic
Jankiewicz, Kasia
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2312_15120
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Generalized Residual Finiteness of Groups
Brody, Nic
Jankiewicz, Kasia
Group Theory
20E26, 20F65
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.
title Generalized Residual Finiteness of Groups
topic Group Theory
20E26, 20F65
url https://arxiv.org/abs/2312.15120