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Residual finiteness growths of Lamplighter groups

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arxiv 1909.03535 v2 pith:R7DTGXSI submitted 2019-09-08 math.GR

Khalid Bou-Rabee , Junjie Chen , Anastasiia Timashova This is my paper · ORCID
classification math.GR
keywords lamplighterfinitenessgroupsresidualgroupgrowthbestbounds
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Residual finiteness growth gives an invariant that indicates how well-approximated a finitely generated group is by its finite quotients. We briefly survey the state of the subject. We then improve on the best known upper and lower bounds for lamplighter groups. Notably, any lamplighter group has super-linear residual finiteness growth. In our proof, we quantify a congruence subgroup property for lamplighter groups.

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Cited by 1 Pith paper

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  1. Residual Finiteness Growth in Two-Step Nilpotent Groups

    math.GR 2025-05 conditional novelty 7.0 of 10

    For two-step nilpotent groups, residual finiteness growth is at most log^{d+1}, with d an invariant of the complex Mal'cev completion, and is exactly log^{d+1} when the commutator subgroup has rank at most 2.

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