Exact residual finiteness growth conjecture for torsion-free nilpotent groups

From papers

Let GG be a torsion-free nilpotent group, and let δ\delta be the constant in the previously established upper bound for the residual finiteness growth RFG\operatorname{RF}_G. Exact residual finiteness growth conjecture. For every torsion-free nilpotent group GG it holds that

RFG=logδ.\operatorname{RF}_G=\log^\delta.

The paper presents this as the conjecture that the cited upper bound is exact; the preceding theorem establishes the corresponding restricted growth function using normal subgroups containing GpG^p, but not the asserted equality for RFG\operatorname{RF}_G itself.

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Sources & referencesView supporting material

Primary source

Jonas Deré, Joren Matthys and Lukas Vandeputte, “Residual Finiteness Growth in Virtually Nilpotent Groups”, arXiv:2512.16585 (2026).

Additional references

3 papers in this index state this conjecture (2025). The statement above is taken from the most recent of them; the others are arXiv:2510.21387, arXiv:2505.21090.

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