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arXiv · 2402.03556

On the spectrum of residual finiteness growth functions

Henry Bradford
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Abstract

In [K. Bou-Rabee, B. Seward, J. Reine Angwe. Math. 2016] Bou-Rabee and Seward constructed examples of finitely generated residually finite groups $G$ whose residual finiteness growth function $\mathcal{F}_G$ can be at least as fast as any prescribed function. In this note we describe a modified version of their construction, which allows us to give a complementary upper bound on $\mathcal{F}_G$. As such, every nondecreasing function at least $\exp ( n \log (n)^2 \log \log (n)^{1+\epsilon} )$ is close to the residual finiteness growth function of some finitely generated group. We also have similar result for the full residual finiteness growth function and for the divisibility function.

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Henry Bradford. 2024-02-05. On the spectrum of residual finiteness growth functions. https://arxiv.org/abs/2402.03556

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