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arXiv · 2312.15120

Generalized Residual Finiteness of Groups

Nic Brody·Kasia Jankiewicz
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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.

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Nic Brody, Kasia Jankiewicz. 2023-12-22. Generalized Residual Finiteness of Groups. https://arxiv.org/abs/2312.15120

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