Some small cancellation properties of random groups

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dc.creatorOllivier, Yann
dc.date2004-09-14
dc.date.accessioned2026-07-07T05:12:06Z
dc.date.available2026-07-07T05:12:06Z
dc.descriptionWe work in the density model of random groups. We prove that they satisfy an isoperimetric inequality with sharp constant $1-2d$ depending upon the density parameter $d$. This implies in particular a property generalizing the ordinary $C'$ small cancellation condition, which could be termed ``macroscopic small cancellation''. This also sharpens the evaluation of the hyperbolicity constant $δ$. As a consequence we get that the standard presentation of a random group at density $d<1/5$ satisfies the Dehn algorithm and Greendlinger's Lemma, and that it does not for $d>1/5$.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0409226
dc.identifierhttp://arxiv.org/abs/math/0409226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72466
dc.subjectGroup Theory
dc.subject20F05,20F06,20P05,20F67
dc.titleSome small cancellation properties of random groups
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