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Proceedings of the American Mathematical Society

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On recognising certain one relation presentations


Authors: James McCool and Alfred Pietrowski
Journal: Proc. Amer. Math. Soc. 36 (1972), 31-33
MSC: Primary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1972-0306333-4
MathSciNet review: 0306333
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Abstract: An algorithm is described to determine, given a finite presentation $ \Pi $ of a one relation group G whose commutator subgroup is finitely generated, whether or not $ \Pi $ is a one relation presentation.


References [Enhancements On Off] (What's this?)

  • [1] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617. MR 0207802 (34:7617)
  • [2] J. McCool and A. Pietrowski, On free products with amalgamation of two infinite cyclic groups, J. Algebra 18 (1971), 377-383. MR 0280576 (43:6296)
  • [3] D. I. Moldavanskiĭ, Certain subgroups of groups with one defining relation, Sibirsk. Mat. Ž. 8 (1967), 1370-1384=Siberian Math. J. 8 (1967), 1039-1048. MR 36 #3862. MR 0220810 (36:3862)
  • [4] J. H. C. Whitehead, On equivalent sets of elements in a free group, Ann. of Math. (2) 37 (1936), 782-800. MR 1503309

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DOI: https://doi.org/10.1090/S0002-9939-1972-0306333-4
Article copyright: © Copyright 1972 American Mathematical Society

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