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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Widths of Subgroups
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by Rita Gitik, Mahan Mitra, Eliyahu Rips and Michah Sageev PDF
Trans. Amer. Math. Soc. 350 (1998), 321-329 Request permission

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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Additional Information
  • Rita Gitik
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Email: ritagtk@math.lsa.umich.edu
  • Mahan Mitra
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • Email: mitra@math.berkeley.edu
  • Eliyahu Rips
  • Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel
  • Email: rips@sunset.huji.ac.il
  • Michah Sageev
  • Affiliation: Department of Mathematics, University of Southampton, Southampton, England
  • MR Author ID: 366122
  • Email: mes@maths.soton.ac.uk
  • Received by editor(s): September 19, 1995
  • Received by editor(s) in revised form: March 25, 1996
  • Additional Notes: Research of the first author supported in part by NSF grant DMS 9022140.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 321-329
  • MSC (1991): Primary 20F32, 57M07
  • DOI: https://doi.org/10.1090/S0002-9947-98-01792-9
  • MathSciNet review: 1389776