2017
DOI: 10.1142/s021819671750014x
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From local to global conjugacy of subgroups of relatively hyperbolic groups

Abstract: Abstract. Suppose that a finitely generated group G is hyperbolic relative to a collection of subgroups P = {P1, . . . , Pm}. Let H1, H2 be subgroups of G such that H1 is relatively quasiconvex with respect to P and H2 is not parabolic. Suppose that H2 is elementwise conjugate into H1. Then there exists a finite index subgroup of H2 which is conjugate into H1. The minimal length of the conjugator can be estimated.In the case where G is a limit group, it is sufficient to assume only that H1 is a finitely genera… Show more

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Cited by 3 publications
(3 citation statements)
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References 14 publications
(17 reference statements)
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“…Thus, there exists such a neighborhood V. Then there exists an open neighborhood O ⊆ V of identity 1 H such that O (2) ⊆ V. Then ϕ((H 0 ∩ O) (2) ) ⊆ Ell(G S). Arguing as in the proof of Theorem A starting from (9), we obtain that there exists a relatively open subgroup A ≤ H 0 such that ϕ(A) is finite and A is normal in H 0 . Let A be an open subset of H such that H 0 ∩ A = A.…”
Section: Proof Of a Strong Version Of Theorem Amentioning
confidence: 85%
“…Thus, there exists such a neighborhood V. Then there exists an open neighborhood O ⊆ V of identity 1 H such that O (2) ⊆ V. Then ϕ((H 0 ∩ O) (2) ) ⊆ Ell(G S). Arguing as in the proof of Theorem A starting from (9), we obtain that there exists a relatively open subgroup A ≤ H 0 such that ϕ(A) is finite and A is normal in H 0 . Let A be an open subset of H such that H 0 ∩ A = A.…”
Section: Proof Of a Strong Version Of Theorem Amentioning
confidence: 85%
“…Also, O. Bogopolski and K-U. Bux in [5] proved that surface groups are conjugacy subgroup separable.…”
Section: Introductionmentioning
confidence: 98%
“…After this paper was submitted Bogopolski and Bux put the paper [5] into arxiv, where they gave independent prove of Theorems 1.2 and 1.3 in [5, Lemma 6.2 and Corollary C] for torsion free groups. Our methods allow us to avoid the assumption of torsion freeness.…”
Section: Introductionmentioning
confidence: 99%