Abstract
We study the problem of finite approximability with respect to conjugacy of amalgamated free products by a normal subgroup and prove the following assertions. A) IfG is the amalgamated free productG=G 1*H G 2 of polycyclic groupsG 1 andG 2 by a normal subgroupH, whereH is an almost free Abelian group of rank 2, thenG is finitely approximate with respect to conjugacy. B) (i) IfG 1 =G 2 =L is a polycyclic group andG=G 1*H G 2 is the amalgamated product of two copies of the groupL by a normal subgroupH, thenG is finitely approximable with respect to conjugacy. (ii) IfG is an amalgamated free productG=G 1*H G 2 of polycyclic groupsG 1 andG 2 by a normal subgroupH, whereH is central inG 1 orG 2, thenG is finitely approximable with respect to conjugacy.
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Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 525–535, October, 1995.
This work was partially supported by the INTAS-94-3420 Grant “Geometric Theory of Groups.”
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Zalesskii, P.A., Tavgen', O.I. Closed orbits and finite approximability with respect to conjugacy of free amalgamated products. Math Notes 58, 1042–1048 (1995). https://doi.org/10.1007/BF02305092
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DOI: https://doi.org/10.1007/BF02305092