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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 93, Issue 2
  • March 1983, pp. 247-251

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

  • Gilbert Baumslag (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100060527
  • Published online: 24 October 2008
Abstract

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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(1)G. Baumslag On generalised free products. Math. Z. 78 (1962), 423438.

(2)G. Baumslag On the residual finiteness of generalised free products of nilpotent groups. Trans. Amer. Math. Soc. 106 (1963), 193209.

(3)G. Baumslag Positive one-relator groups. Trans. Amer. Math. Soc. 156 (1971), 165183.

(4)G. Baumslag , E. Dyer and A. Heller The topology of discrete groups. J. Pure and Appl. Algebra, 16 (1980), 147.

(5)K. N. Frederick The hopfian property for a class of fundamental groups. Comm. Pure Appl. Math. 16 (1963), 18.

(9)W. Magnus Das Identitatsproblem fur Gruppen mit einer definierenden Relation. Math Annalen, 106 (1932), 295307.

(10)W. Magnus Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring. Math. Annalen, 111 (1935), 259280.

(11)W. Magnus Uber freie Faktorgruppen und freie Untergruppen gegebener Gruppen. Monatsh. Math. 47 (1939), 105115.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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