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Baumslag–Solitar groups and residual nilpotence
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 2 / May 2023
- Published online by Cambridge University Press:
- 16 June 2023, pp. 532-547
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- Article
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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.
