All countable groups have cubic presentations
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- by Matthew A. Marcus PDF
- Proc. Amer. Math. Soc. 93 (1985), 411-413 Request permission
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
- 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
- Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89, Springer-Verlag, Berlin-New York, 1977. MR 0577064 J. M. Montesinos, Representing $3$-manifolds by a universal branching set, Math Proc. Cambridge (to appear).
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 411-413
- MSC: Primary 20F05; Secondary 57M05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0773991-9
- MathSciNet review: 773991