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Nonresidually Finite One-Relator Groups

Stephen Meskin
Transactions of the American Mathematical Society
Vol. 164 (Feb., 1972), pp. 105-114
DOI: 10.2307/1995962
Stable URL: http://www.jstor.org/stable/1995962
Page Count: 10
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Nonresidually Finite One-Relator Groups
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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 $u^{-1}v^1 uv^m$ 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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