2005
DOI: 10.1016/j.jalgebra.2004.10.022
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Conjugacy separability of certain Seifert 3-manifold groups

Abstract: It is well known that Seifert 3-manifold groups are residually finite. Niblo [J. Pure Appl. Algebra 78 (1992) 77-84] showed that they are double coset separable. Applying this result we show that, except for some special cases, most of the Seifert 3-manifold groups are conjugacy separable.  2004 Elsevier Inc. All rights reserved.

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Cited by 7 publications
(14 citation statements)
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“…For Seifert 3-manifolds with non-trivial boundary, a positive conclusion follows immediately form work of Ribes, Segal and Zalesskii [11]. In the case of closed Seifert 3-manifolds, the fact that almost all Seifert 3-manifold groups with orientable surfaces (briefly, Seifert groups over orientable surfaces) are conjugacy separable was shown in [2]. In this paper we complete the picture by showing all Seifert groups over non-orientable surfaces are also conjugacy separable.…”
Section: Introductionmentioning
confidence: 58%
See 1 more Smart Citation
“…For Seifert 3-manifolds with non-trivial boundary, a positive conclusion follows immediately form work of Ribes, Segal and Zalesskii [11]. In the case of closed Seifert 3-manifolds, the fact that almost all Seifert 3-manifold groups with orientable surfaces (briefly, Seifert groups over orientable surfaces) are conjugacy separable was shown in [2]. In this paper we complete the picture by showing all Seifert groups over non-orientable surfaces are also conjugacy separable.…”
Section: Introductionmentioning
confidence: 58%
“…Niblo (1992) [9] improved this result by showing that these groups are double coset separable. In Allenby, Kim and Tang (2005) [2] it was shown that all but two types of groups in the orientable case are conjugacy separable. Martino (2007) [7] using topological results showed that Seifert groups are conjugacy separable.…”
mentioning
confidence: 99%
“…Additionally, these properties are related to the problem of lifting immersed subspaces of topological spaces to embedded subspaces of finite covers. Recently, [1] have proved that certain Seifert 3-manifold groups are conjugacy separable and in this paper we prove that all Seifert 3-manifold groups are conjugacy separable.…”
Section: Introductionmentioning
confidence: 85%
“…where [1] φ i is understood to be a twisted-φ i conjugacy class in S. By hypothesis, each [1] φ i is closed in S and thence in G. Thus each g i [1] φ i is closed in G and thus so is the (finite) union. Thus we have shown that every conjugacy class in G is closed, which is another way of saying that G is conjugacy separable.…”
Section: Virtual Surface Groupsmentioning
confidence: 99%
“…However generalized free products of polycyclic-by-finite groups, amalgamating central subgroups, are conjugacy separable [8]. Recently, Allenby, Kim, and Tang [1] considered the case when the amalgamated subgroup is a direct product of two cyclic groups and showed that most of Seifert groups are conjugacy separable.…”
Section: Introductionmentioning
confidence: 99%