Some small cancellation properties of random groups

Details Some small cancellation properties of random groups Some small cancellation properties of random groups

2004-09-14

arxiv.org/abs/math/0409226v1

Mathematics

Group Theory

11 pages

Scientific paper

We 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 $\delta$. 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 $d>1/5$.

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