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Conjugacy Separability of Generalized Free Products of Certain Conjugacy Separable Groups

Published online by Cambridge University Press:  20 November 2018

C. Y. Tang
C. Y. Tang*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1
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Abstract

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We prove that generalized free products of finitely generated free-byfinite or nilpotent-by-finite groups amalgamating a cyclic subgroup areconjugacy separable. Applying this result we prove a generalization of a conjecture of Fine and Rosenberger [7] that groups of F-type are conjugacy separable.

Keywords

20E0620E2620E0520F0520F18
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 120 - 127
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Allenby, R. B. J. T., Conjugacy separability of a class of \-relator products, Proc. Amer. Math. Soc. 116(1993), 621–628.Google Scholar
2. Allenby, R. B. J. T. and Tang, C. Y., The residual finiteness of some \-relator groups with torsion, J. Algebra 71(1981), 132–140.Google Scholar
3. Allenby, R. B. J. T. and Tang, C. Y., Conjugacy separability of certain 1 -relator groups with torsion, J. Algebra 103(1986), 619–637.Google Scholar
4. Dyer, J. L., Separating conjugates in free-by-finite groups, J. London Math. Soc. (2) 20(1979), 215–221.Google Scholar
5. Dyer, J. L., Separating conjugates in amalgamated free products and HNN extensions, J. Austral. Math. Soc. Ser. A 29(1980), 35–51.Google Scholar
6. Fine, B. and Rosenberger, G., Conjugacy separability of Fuchsian groups and related questions, Contemp. Math. 109(1990), 11–18.Google Scholar
7. Fine, B., Generalized algebraic properties of Fuchsian groups, Groups, St. Andrews 1, London Math. Soc. Lecture Note Series 160, 1989.Google Scholar
8. Formanek, E., Conjugacy separability in poly cyclic groups, J. Algebra 42(1976), 1–10.Google Scholar
9. Magnus, W., Karrass, A. and Solitar, D., Combinatorial groups theory, Pure Appl. Math. XIII, Wiley- Interscience, New York, London, Sydney, 1966.Google Scholar
10. Remeslennikov, V. M., Conjugacy in poly cyclic groups, Algebra i Logika 8(1969), 712–725, Russian; Translation: Algebra and Logic 8(1969), 404–11.Google Scholar
11. Ribes, L. and Zalesskii, P. A., On the profinite topology on a free group, Bull. London Math. Soc. 25(1993), 37–43.Google Scholar
12. Stebe, P. F., Residual solvability of an equation in nilpotent groups, Proc. Amer. Math. Soc. 54(1976), 57–58.Google Scholar