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
Conjugacy separability of generalized free products of surface groups
โ 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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โฆ 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. @
๐ SIMILAR VOLUMES
We first prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a cyclic subgroup. Applying this result, we show that tree products of a finite number of conjugacy separable, residually finitely generated torsion-free nilpotent gr
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
A group G is said to be conjugacy separable if for each pair of elements x y โ 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