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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

All countable groups have cubic presentations


Author: Matthew A. Marcus
Journal: Proc. Amer. Math. Soc. 93 (1985), 411-413
MSC: Primary 20F05; Secondary 57M05
MathSciNet review: 773991
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a group with presentation such that each generator occurs at most countably many times in the set of relations. Then for all $ n \geqslant 3$, $ G$ is $ n$-ic. In particular, for all $ n \geqslant 3$, countable groups have $ n$-ic presentations.


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

  • [1] L. Neuwirth, Some algebra for 3-manifolds, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969), Markham, Chicago, Ill., 1970, pp. 179–184. MR 0276978 (43 #2716)
  • [2] Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89. MR 0577064 (58 #28182)
  • [3] J. M. Montesinos, Representing $ 3$-manifolds by a universal branching set, Math Proc. Cambridge (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0773991-9
PII: S 0002-9939(1985)0773991-9
Keywords: Presentations of groups
Article copyright: © Copyright 1985 American Mathematical Society