Separation of relatively quasiconvex subgroups
نویسندگان
چکیده
منابع مشابه
Separation of Relatively Quasiconvex Subgroups
Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that...
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For relatively hyperbolic groups, we investigate conditions under which the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1 ∗Q1∩Q2 Q2. Our results generalized known combination theorems for quasiconvex subgroups of word-hyperbolic groups. Some applications are presented. In addition, it is proved that the intersection of quasiconvex subgroups is qua...
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We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. W...
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A graph group, or right-angled Artin group, is a group given by a presentation where the only relators are commutators of the generators. A graph group presentation corresponds in a natural way to a simplicial graph, with each generator corresponding to a vertex, and each commutator relator corresponding to an edge. Suppose that G is a graph group whose corresponding graph is a tree and H is a ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2009
ISSN: 0030-8730
DOI: 10.2140/pjm.2010.244.309