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- W2891158562 abstract "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." @default.
- W2891158562 created "2018-09-27" @default.
- W2891158562 creator A5049399184 @default.
- W2891158562 date "2018-09-21" @default.
- W2891158562 modified "2023-09-27" @default.
- W2891158562 title "Residual dimension of nilpotent groups: correction to Effective separability of finitely generated nilpotent groups" @default.
- W2891158562 hasPublicationYear "2018" @default.
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