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

  • Gilbert Baumslag (a1)
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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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(2)Baumslag, G.On the residual finiteness of generalised free products of nilpotent groups. Trans. Amer. Math. Soc. 106 (1963), 193209.
(3)Baumslag, G.Positive one-relator groups. Trans. Amer. Math. Soc. 156 (1971), 165183.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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