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Baumslag–Solitar groups and residual nilpotence
Published online by Cambridge University Press: 16 June 2023
Abstract
Let G be a Baumslag–Solitar group. We calculate the intersection $\gamma_{\omega}(G)$ of all terms of the lower central series of G. Using this, we show that $[\gamma_{\omega}(G),G]=\gamma_{\omega}(G)$, thus answering a question of Bardakov and Neschadim [1]. For any $c \in \mathbb{N}$, with $c \geq 2$, we show, by using Lie algebra methods, that the quotient group $\gamma_{c}(G)/\gamma_{c+1}(G)$ of the lower central series of G is finite.
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- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.