Free subgroups of certain one-relator groups defined by positive words

Abstract

Let ℒ be the class of those groups G which can be presented in the formwhere u and v are positive words in the given generators. Here a word w is termed positive if only non-negative powers of a, b,…, c occur in w. If each generator occurs with exponent sum zero in uv-1, we term the ℒ-group G a -group. This class contains, in particular, the class X of those groups G which can be presented in the formwhere u and v are positive words, and where [u, v] is the commutator uvu-1v-1.