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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  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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- Gilbert Baumslag, On the residual finiteness of generalised free products of nilpotent groups, Trans. Amer. Math. Soc. 106 (1963), 193-209. MR 26 #2489. MR 0144949 (26:2489)
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- Gilbert Baumslag and Donald Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199-201. MR 26 #204. MR 0142635 (26:204)
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- P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595-622. MR 22 #1618. MR 0110750 (22:1618)
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- Graham Higman, A finitely related group with an isomorphic proper factor group, J. London Math. Soc. 25 (1951), 59-61. MR 12, 390. MR 0038347 (12:390b)
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- Paul E. Schupp, On the substitution problem for free groups, Proc. Amer. Math. Soc. 23 (1969), 421-423. MR 39 #6963. MR 0245657 (39:6963)
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- Peter Stebe, Residual finiteness of a class of knot groups, Comm. Pure Appl. Math. 21 (1968), 563-583. MR 38 #5902. MR 0237621 (38:5902)
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- M. J. Wicks, Commutators in free products, J. London Math. Soc. 37 (1962), 433-444. MR 26 #179. MR 0142610 (26:179)
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Additional Information
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
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