Abstract
LetG be a free product of free groups with cyclic amalgamation. In this note we prove a criterion for the groupG to be a residually finitep-group. Other residual properties of the groupG are also established.
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References
G. Baumslag, “On the residual finiteness of generalized free products of nilpotent groups,”Trans. Amer. Math. Soc.,106, 193–209 (1963).
J. Dyer, “Separating conjugates in amalgamated free products and HNN-extensions,”J. Austral. Math. Soc. Ser. A,29, No. 1, 35–51 (1980).
A. Brunner, R. Burns, and D. Solitar, “The subgroup separability of free products of two free groups with cyclic amalgamation,”Contemp. Math.,33, 90–115 (1984).
D. Gildenhuys, “One-relator groups that are residually of prime power order,”J. Austral. Math. Soc. Ser. A,19, 385–409 (1975).
P. Stebe, “Conjugacy separability of certain free products with amalgamation,”Trans. Amer. Math. Soc.,156, 119–129 (1971).
K. W. Gruenberg, “Residual properties of infinite soluble groups,”Proc. London Math. Soc.,7, 29–62 (1957).
G. Higman, “Amalgams ofp-group,”J. Algebra,1, 301–305 (1964).
R. C. Lyndon and P. E. Shupp,Combinatorial Group Theory, Springer-Verlag, Berlin-New York (1977).
G. Baumslag, “On the residual nilpotence of certain one-relator groups,”Comm. Pure Appl. Math.,21, No. 5, 491–506 (1968).
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Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 3–8, July, 1998.
The author wishes to thank Professor D. I. Moldavanskii for a number of important remarks and valuable advice in the preparation of this paper.
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Azarov, D.N. On the residual nilpotence of free products of free groups with cyclic amalgamation. Math Notes 64, 3–7 (1998). https://doi.org/10.1007/BF02307189
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DOI: https://doi.org/10.1007/BF02307189