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Residual finiteness of certain 1-relator groups: extensions of results of Gilbert Baumslag

Published online by Cambridge University Press:  24 October 2008

R. B. J. T. Allenby  and
C. Y. Tang
R. B. J. T. Allenby
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds L82 9JT
C. Y. Tang
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada
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Extract

Let be the class of groups which can be presented in the form

where u, v are positive words on the generators g, h, …, k and where each generator appears in uv−1 with zero exponent sum. Let be the class of groups which can be presented in the form

where u, v are words (not necessarily positive) on the disjoint sets of generators c1, …, cm and d1, …, dn and where [u, v] = u−1v−1uv.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 225 - 230
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Allenby, R. B. J. T., Moser, L. E. and Tang, C. Y.. The residual finiteness of certain one-relator groups. Proc. Amer. Math. Soc. 78 (1980), 8–10.CrossRefGoogle Scholar
[2]Allenby, R. B. J. T. and Tang, C. Y.. The residual finiteness of some one-relator groups with torsion. J. Algebra 71 (1981), 132–140.CrossRefGoogle Scholar
[3]Allenby, R. B. J. T. and Tang, C. Y.. Residually finite one-relator groups with torsion. Arch. Math. 37 (1981), 97–105.CrossRefGoogle Scholar
[4]Baumslag, G.. On the residual finiteness of generalised free products of nilpotent groups. Trans. Amer. Math. Soc. 106 (1963), 193–209.CrossRefGoogle Scholar
[5]Baumslag, G.. Residually finite one-relator groups. Bull. Amer. Math. Soc. 73 (1967), 618–620.CrossRefGoogle Scholar
[6]Baumslag, G.. Some problems on one-relator groups. Proc. of the Second Int. Conference on the Theory of Groups. Lecture Notes in Math. vol. 372 (Springer-Verlag, 1974), 75–81.Google Scholar
[7]Baumslag, G.. Free subgroups of certain one-relator groups defined by positive words. Math. Proc. Cambridge Philos. Soc. 93 (1983), 247–251.CrossRefGoogle Scholar
[8]Collins, D. J.. Some one-relator Hopfian groups. Trans. Amer. Math. Soc. 235 (1978), 363–374.CrossRefGoogle Scholar
[9]Magnus, W., Kabbass, A. and Solitar, D.. Combinatorial Group Theory: Presentations of groups in terms of generators and relations (Wiley-Interscience, 1966).Google Scholar
[10]Meskin, S.. Nonresidually finite one-relator groups. Trans. Amer. Math. Soc. 164 (1972), 105–114.CrossRefGoogle Scholar
[11]Newman, B. B.. Some results on one-relator groups. Bull. Amer. Math. Soc. 74 (1968), 568–571.CrossRefGoogle Scholar
[12]Rosenberger, G.. Über Gruppen mit einer definierenden Relation. Math. Z. 155 (1977), 71–77.CrossRefGoogle Scholar
[13]Stebe, P.. Conjugacy separability of certain free products with amalgamation. Trans. Amer. Math. Soc. 156 (1971), 119–129.CrossRefGoogle Scholar
[14]Stebe, P.. Residual finiteness of a class of knot groups. Comm. on Pure and Appl. Math. 21 (1968), 563–583.CrossRefGoogle Scholar