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dc.contributor.authorChiodo, Maurice
dc.contributor.authorVyas, Rishi
dc.date.accessioned2018-09-20T12:05:44Z
dc.date.available2018-09-20T12:05:44Z
dc.date.issued2018-09-01
dc.identifier.issn1433-5883
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/280509
dc.description.abstract<jats:title>Abstract</jats:title> <jats:p>We show that a construction by Aanderaa and Cohen used in their proof of the Higman Embedding Theorem preserves torsion length. We give a new construction showing that every finitely presented group is the quotient of some <jats:inline-formula id="j_jgth-2018-0022_ineq_9999_w2aab3b7e4488b1b6b1aab1c15b1b1Aa"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>C</m:mi> <m:mo>′</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>6</m:mn> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_jgth-2018-0022_eq_0139.png" /> <jats:tex-math>{C^{\prime}(1/6)}</jats:tex-math> </jats:alternatives> </jats:inline-formula> finitely presented group by the subgroup generated by its torsion elements. We use these results to show there is a finitely presented group with infinite torsion length which is <jats:inline-formula id="j_jgth-2018-0022_ineq_9998_w2aab3b7e4488b1b6b1aab1c15b1b3Aa"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>C</m:mi> <m:mo>′</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>6</m:mn> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_jgth-2018-0022_eq_0139.png" /> <jats:tex-math>{C^{\prime}(1/6)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and thus word-hyperbolic and virtually torsion-free.</jats:p>
dc.languageen
dc.publisherWalter de Gruyter GmbH
dc.titleTorsion, torsion length and finitely presented groups
dc.typeArticle
prism.endingPage971
prism.issueIdentifier5
prism.publicationDate2018
prism.publicationNameJournal of Group Theory
prism.startingPage949
prism.volume21
dc.identifier.doi10.17863/CAM.27879
dcterms.dateAccepted2018-05-04
rioxxterms.versionofrecord10.1515/jgth-2018-0022
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2018-09-01
dc.identifier.eissn1435-4446
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (659102)
cam.issuedOnline2018-06-19
rioxxterms.freetoread.startdate2019-06-19


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