Let ℒ be the class of those groups G which can be presented in the form
where 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 form
where u and v are positive words, and where [u, v] is the commutator uvu-1v-1.
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