Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

R. B. J. T. Allenbya1 and C. Y. Tanga2

a1 Department of Pure Mathematics, University of Leeds, Leeds L82 9JT

a2 Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada

Let S0305004100062782_inline1 be the class of groups which can be presented in the form

S0305004100062782_eqnU1

where u, v are positive words on the generators g, h, …, k and where each generator appears in uv−1 with zero exponent sum. Let S0305004100062782_inline2 be the class of groups which can be presented in the form

S0305004100062782_eqnU2

where 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.

(Received September 06 1983)

(Revised June 19 1984)