Residual dimension of nilpotent groups: correction to "Effective separability of finitely generated nilpotent groups"

Mark Pengitore

Published 2018-09-21Version 1

The functions $\text{F}_{G}(n)$ and $\text{Conj}_{G}(n)$ measure the asymptotic behavior of residual finiteness and conjugacy separability for a finitely generated group $G$, respectively. In previous work, the author claimed a characterization for $\text{F}_{G}(n)$ and lower asymptotic bounds for $\text{Conj}_{G}(n)$ when $G$ is a finitely generated nilpotent group. However, a counterexample to the characterization of $\text{F}_{G}(n)$ for finitely generated nilpotent groups was communicated to the author which also had consequences to the lower asymptotic bound provided for $\text{Conj}_{G}(n)$. Subsequently, the statements of the asymptotic characterization of $\text{F}_{G}(n)$ and the asymptotic lower bound for $\text{Conj}_{G}(n)$ along with their proofs are incorrect. In this article, we provide correct lower asymptotic bounds for $\text{F}_{G}(n)$ and asymptotic lower bounds for $\text{Conj}_{G}(n)$ when $G$ is a finitely generated nilpotent group.