Solvable subgroups of groups of polynomial automorphisms - MathOverflow most recent 30 from http://mathoverflow.net2013-05-25T04:44:23Zhttp://mathoverflow.net/feeds/question/2502http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/2502/solvable-subgroups-of-groups-of-polynomial-automorphismsSolvable subgroups of groups of polynomial automorphismsanon2009-10-25T19:37:27Z2009-11-23T04:28:43Z
<p>Does every finitely generated free solvable group embed into the group of polynomial automorphisms of some C^n?</p>
http://mathoverflow.net/questions/2502/solvable-subgroups-of-groups-of-polynomial-automorphisms/6530#6530Answer by Mariano Suárez-Alvarez for Solvable subgroups of groups of polynomial automorphismsMariano Suárez-Alvarez2009-11-23T04:28:43Z2009-11-23T04:28:43Z<p>Wilhelm Magnus (W. Magnus, Über $n$-dimensionale Gittertransformationen. Acta Math. 64 (1935), no. 1, 353--367.) seems to have shown that the free metabelian group on $n$ generators has a faithful representation of degree $2$. It follows that there is a copy of the free solvable group on $n$ generators and of derived length $2$ inside $GL_2(\mathbb{C})$.</p>
<p>That answers your question affirmatively in a special case.</p>