Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T14:05:11.299Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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