Residual finiteness of certain 1-relator groups: extensions of results of Gilbert Baumslag

Abstract

Let be the class of groups which can be presented in the formwhere u, v are positive words on the generators g, h, …, k and where each generator appears in uv−1 with zero exponent sum. Let be the class of groups which can be presented in the formwhere u, v are words (not necessarily positive) on the disjoint sets of generators c1, …, cm and d1, …, dn and where [u, v] = u−1v−1uv.