Baumslag-Solitar groups and residual nilpotence

Abstract

Let G be a Baumslag-Solitar group. We calculate the intersection γ w pGq of all terms of the lower central series of G. Using this, we are able to show that rγ w pGq, Gs " γ w pGq; thus answering a question of Bardakov and Neschadim [1]. Finally, for any c P N, with c ě 2, we show that the quotient group γ c pGq{γ c`1 pGq of the lower central series of G is finite.