A special residually finite group - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T17:39:29Z http://mathoverflow.net/feeds/question/41653 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/41653/a-special-residually-finite-group A special residually finite group anon 2010-10-10T06:17:26Z 2010-10-11T05:27:37Z <p>Is there an example of a finitely generated (infinite) residually finite group \$\Gamma\$ for which every linear representation of \$\Gamma\$ has finite image?</p> http://mathoverflow.net/questions/41653/a-special-residually-finite-group/41659#41659 Answer by Mustafa Gokhan Benli for A special residually finite group Mustafa Gokhan Benli 2010-10-10T07:02:42Z 2010-10-10T19:51:42Z <p>A group \$G\$ is <strong>just infinite</strong> if it is infinite but every proper quotient is finite.</p> <p>Clearly a just infinite group which is not linear has the property that its image under any linear representation is finite. Thus any group which is finitely generated, residually finite, not linear and just infinite is an example of what you want: for instance, the <a href="http://en.wikipedia.org/wiki/Grigorchuk_group" rel="nofollow">Grigorchuk group</a>.</p>