Baumslag-Solitar groups and residual nilpotence

Abstract

For a Baumslag-Solitar group $G$ we calculate the intersection ${\gamma }_w(G)$ of all terms of the lower central sequence of $G$.Using this we are able to show that $[{\gamma }_w(G),G]={\gamma }_w(G)$ thus answering a question of Bardakov and Neschadim. Finally we show that the quotient groups ${\gamma }_c(G)/{\gamma }_{c+1}(G)$ of the lower central series of $G$ are finite.

14 pages, All comments welcome, minor changes, various typos corrected