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ISSN 1088-6850(e) ISSN 0002-9947(p)

Widths of Subgroups

Author(s): Rita Gitik; Mahan Mitra; Eliyahu Rips; Michah Sageev
Journal: Trans. Amer. Math. Soc. 350 (1998), 321-329.
MSC (1991): Primary 20F32, 57M07
MathSciNet review: 1389776
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Abstract: We say that the width of an infinite subgroup $H$ in $G$ is $n$ if there exists a collection of $n$ essentially distinct conjugates of $H$ such that the intersection of any two elements of the collection is infinite and $n$ is maximal possible. We define the width of a finite subgroup to be $0$ . We prove that a quasiconvex subgroup of a negatively curved group has finite width. It follows that geometrically finite surfaces in closed hyperbolic $3$ -manifolds satisfy the $k$ -plane property for some $k$ .

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