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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonresidually finite one-relator groups


Author: Stephen Meskin
Journal: Trans. Amer. Math. Soc. 164 (1972), 105-114
MSC: Primary 20.10
MathSciNet review: 0285589
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Abstract: The study of one-relator groups includes the connections between group properties and the form of the relator. In this paper we discuss conditions on the form $ {u^{ - 1}}{v^l}u{v^m}$ which force the corresponding one-relator groups to be nonresidually finite, i.e. the intersection of the normal subgroups of finite index to be nontrivial. Moreover we show that these forms can be detected amongst the words of a free group.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0285589-5
PII: S 0002-9947(1972)0285589-5
Keywords: One-relator groups, residually finite, algorithm, free groups, word form
Article copyright: © Copyright 1972 American Mathematical Society