Does $C'\left(\frac{5}{11}\right)$ imply exponential growth? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T04:22:09Z http://mathoverflow.net/feeds/question/109288 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109288/does-c-left-frac511-right-imply-exponential-growth Does $C'\left(\frac{5}{11}\right)$ imply exponential growth? Elisabeth Fink 2012-10-10T10:59:21Z 2012-10-10T15:03:10Z <p>I came across this rather week small cancellation condition $C'\left(\frac{5}{11}\right)$ of a group $G$. It has been proved that $C'\left(\frac16\right)$ is enough for $G$ to contain free subgroups. I was therefore wondering if $\frac{5}{11}$ is maybe enough to still have exponential growth. </p> <p>Does anyone know of any related papers or results?</p> http://mathoverflow.net/questions/109288/does-c-left-frac511-right-imply-exponential-growth/109294#109294 Answer by Mark Sapir for Does $C'\left(\frac{5}{11}\right)$ imply exponential growth? Mark Sapir 2012-10-10T12:41:25Z 2012-10-10T15:03:10Z <p>Every finitely presented group has presentation satisfying $C'(1/5)$. Note that $1/5 &lt; 5/11$. See the book by Olshanskii's book "Geometry of defining relations of groups". </p>