Abstract
In this paper, we show that certain generalized free products of nilpotent-by-finite groups are subgroup separable when the amalgamated subgroup is 〈h〉×D where D is in the center of both factors.
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Hall Jr., M.: Coset representations in free groups. Trans. Amer. Math. Soc., 67, 421–432 (1949)
Mal’cev, A. I.: On homomorphisms onto finite groups. Amer. Math. Soc. Transl. (2), 119, 67–79 (1983)
Baumslag, G.: On the residual finiteness of generalized free products of nilpotent groups. Trans. Amer. Math. Soc., 106, 193–209 (1963)
Allenby, R. B. J. T., Gregorac, R. J.: On Locally Extended Residually Finite Groups. Lecture Notes in Mathematics, 319, Springer-Verlag, New York, 1973
Allenby, R. B. J. T., Doniz, D.: A free product of finitely generated nilpotent groups amalgamating a cycle that is not subgroup separable. Proc. Amer. Math. Soc., 124, 1003–1005 (1996)
Gitik, R.: Graphs and separability properties of groups. J. Algebra, 188, 125–143 (1997)
Thurston, W. F.: Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math. Soc., 6, 357–381 (1982)
Baumslag, G.: A non-Hopfian group. Bull. Amer. Math. Soc., 68, 196–198 (1962)
Kim, G., Tang, C. Y.: Conjugacy separability of certain generalized free products of nilpotent groups. Preprint.
Tang, C. Y.: Conjugacy separability of generalized free products of certain conjugacy separable groups. Canad. Math. Bull., 38, 120–127 (1995)
Allenby, R. B. J. T., Tang, C. Y.: The residual finiteness of some one-relator groups with torsion. J. Algebra, 71, 132–140 (1981)
Evans, B.: Cyclic amalgamations of residually finite groups. Pacific J. Math., 55, 371–379 (1974)
Metaftsis, V., Raptis, E.: Subgroup separability of graphs of nilpotent groups. J. Group Theory, 7, 265–273 (2004)
Niblo, G. A., Wise, D.: Subgroup separability, knot groups and graph manifolds. Proc. Amer. Math. Soc., 129, 685–693 (2001)
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Supported by the 2011 Yeungnam University Research Grant; the first author is also supported by the Fundamental Research Funds for the Central Universities (Grant No. XDJK2009C189) and National Natural Science Foundation of China (Grant No. 11271301)
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Zhou, W., Kim, G. Subgroup separability of certain generalized free products of nilpotent-by-finite groups. Acta. Math. Sin.-English Ser. 29, 1199–1204 (2013). https://doi.org/10.1007/s10114-013-0547-3
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DOI: https://doi.org/10.1007/s10114-013-0547-3