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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On $ r$th roots in eighth-groups


Author: Spenser O. Gowdy
Journal: Proc. Amer. Math. Soc. 51 (1975), 253-259
MSC: Primary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1975-0372045-7
MathSciNet review: 0372045
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Abstract: Let $ G$ be an eighth-group having no relators of the form $ R \cong {a^t}$. If $ {X^r} = {a^n}$ where $ a$ is a generator and $ X$ is a word then $ r$ divides $ n$ and $ X = {a^{n/r}}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372045-7
Keywords: Finitely presented groups, generators and relators, Greendlinger's lemma, word problem, conjugacy problem, free groups, free products, small cancellation groups
Article copyright: © Copyright 1975 American Mathematical Society