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  Detecting trivial elements of periodic quotient of hyperbolic groups

Coulon, R. (2018). Detecting trivial elements of periodic quotient of hyperbolic groups. Bulletin de la Société Mathématique de France, 146(4), 745-806. doi:10.24033/bsmf2772.

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Coulon_Detecting trivial elements_2018.pdf (Publisher version), 846KB
 
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Preprint title: A criterion for detecting trivial elements of Burnside groups
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https://doi.org/10.24033/bsmf2772 (Publisher version)
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Coulon, Rémi1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: In this article we give a sufficient and necessary condition to determine whether an element of the free group induces a nontrivial element of the free Burnside
group of sufficiently large odd exponents. Although this result is “well known” among
specialists, it has never been stated with such a level of simplicity. Moreover, our proof highlights some important differences between the Delzant-Gromov approach to the Burnside problems and others that exist. This criterion can be stated without any
knowledge regarding Burnside groups, in particular about the proof of its infiniteness.
Therefore, it also provides a useful tool to study outer automorphisms of Burnside
groups. In addition, we state an analogue result for periodic quotients of torsion-free
hyperbolic groups.

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Language(s): eng - English
 Dates: 2018
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: DOI: 10.24033/bsmf2772
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Title: Bulletin de la Société Mathématique de France
  Abbreviation : Bull. Soc. Math. France
Source Genre: Journal
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Pages: - Volume / Issue: 146 (4) Sequence Number: - Start / End Page: 745 - 806 Identifier: -