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

 

The power problem for groups with one defining relator


Author: James McCool
Journal: Proc. Amer. Math. Soc. 28 (1971), 427-430
MSC: Primary 20.10
MathSciNet review: 0274563
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0274563-5
PII: S 0002-9939(1971)0274563-5
Keywords: Group presentation, one defining relator, generalized word problem, cyclic subgroups
Article copyright: © Copyright 1971 American Mathematical Society