The residual finiteness of certain one-relator groups

Abstract

We prove that the groups ⟨ a , b ; ( a − 1 b l a b m ) t ⟩ \langle a,b;{({a^{ - 1}}{b^l}a{b^m})^t}\rangle , where l , m , t ∈ Z l,m,t \in Z and t ⩾ 2 t \geqslant 2 are residually finite ( R F ) {(_R}F) , thus establishing a conjecture of G. Baumslag [Bull. Amer. Math. Soc. 73 (1967), 618-620].