Generalized Residual Finiteness of Groups

2023/12/22 by Brody, Nic, Jankiewicz, Kasia
#20E26 #20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2312.15120

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.

Related

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