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Arbitrarily large residual finiteness growth
-
Khalid Bou-Rabee
and
Brandon Seward
Published/Copyright:
February 5, 2014
Abstract
The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship between residual finiteness growth and some decision problems in groups, which we apply to our new groups.
Funding source: NSF RTG
Award Identifier / Grant number: DMS-1045119
Funding source: NSF Graduate Student Research Fellowship
Award Identifier / Grant number: DGE 0718128
The first author is grateful to Benson Farb and Ben McReynolds for their endless support and great ideas. The second author would like to thank Jay Williams for an insightful discussion of Neumann's construction.
Received: 2013-5-8
Revised: 2013-10-12
Published Online: 2014-2-5
Published in Print: 2016-1-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- The Minkowski problem, new constant curvature surfaces in ℝ3, and some applications
- The asymptotic expansion of a hypergeometric series coming from mirror symmetry
- Convergence of metrics under self-dual Weyl tensor and scalar curvature bounds
- Bounded sets of sheaves on Kähler manifolds
- Quasiconvexity in relatively hyperbolic groups
- Twisted Hilbert transforms vs Kakeya sets of directions
- Approximation forte en famille
- Arbitrarily large residual finiteness growth
- Big denominators and analytic normal forms
