Limit Groups are Subgroup Conjugacy Separable

2015/11/14 by Chagas, S. C., Zalesskii, P. A.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1511.04607

Abstract

A group G is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of G, there exists a finite quotient of G where the images of these subgroups are not conjugate. We prove that limit groups are subgroup conjugacy separable. We also prove this property for one relator groups of the form R=⟨ a₁,...,a_n| Wⁿ⟩ with n>|W|. The property is also proved for virtual retracts (equivalently for quasiconvex subgroups) of hyperbolic virtually special groups.

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