On the spectrum of residual finiteness growth functions

2024/02/05 by Bradford, Henry · 2 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.03556

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 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 F_G. As such, every nondecreasing function at least exp ( n log (n)² log log (n)^1+ε ) 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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