The power problem for groups with one defining relator
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- by James McCool PDF
- Proc. Amer. Math. Soc. 28 (1971), 427-430 Request permission
Abstract:
It is proved that if $G$ is a group with one defining relator, then the generalized word problem is solvable for every cyclic subgroup of $G$. This result enables the solution of the word problem for groups with one defining relator to be extended to a wider class of groups.References
- Seymour Lipschutz, An extension of Greendlinger’s results on the word problem, Proc. Amer. Math. Soc. 15 (1964), 37–43. MR 160808, DOI 10.1090/S0002-9939-1964-0160808-5
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
- James McCool, The order problem and the power problem for free product sixth-groups, Glasgow Math. J. 10 (1969), 1–9. MR 241512, DOI 10.1017/S0017089500000458
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 427-430
- MSC: Primary 20.10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274563-5
- MathSciNet review: 0274563