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Conjugacy separability of generalized free products of surface groups

โœ Scribed by C.Y. Tang


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
587 KB
Volume
120
Category
Article
ISSN
0022-4049

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โœฆ Synopsis


We prove that generalized free products of two free groups or finitely generated torsion-free nilpotent groups amalgamating a cyclic subgroup are cyclic conjugacy separable. Using this we prove that generalized free products of two surface groups amalgamating a cyclic subgroup are conjugacy separable. We conjecture that generalized free products of two Fuchsian groups amalgamating a cyclic subgroup are conjugacy separable. @


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Conjugacy Separability of Amalgamated Fr
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G and G amalgamating a common subgroup H. The first problem that 1 2 one encounters is that the residual finiteness of G and G does not imply 1 2 w x in general that G is residually finite. Baumslag 1 proved that if G and 1 G are either both free or both torsion-free finitely generated nilpotent 2 g

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In this paper we prove that a free product of conjugacy separable groups A and B, amalgamating a cyclic subgroup, is conjugacy separable if A and B are subgroup separable, cyclic conjugacy separable, 2-free, and residually p-finite, for all prime numbers p. The following result is an example of the

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A group G is said to be conjugacy separable if for each pair of elements x y โˆˆ G such that x and y are not conjugate in G, there exists a finite homomorphic image แธ  of G such that the images of x y are not conjugate in แธ . In this note, we show that the tree products of finitely many conjugacy separa