Solvable subgroups of groups of polynomial automorphisms - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T04:44:23Z http://mathoverflow.net/feeds/question/2502 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/2502/solvable-subgroups-of-groups-of-polynomial-automorphisms Solvable subgroups of groups of polynomial automorphisms anon 2009-10-25T19:37:27Z 2009-11-23T04:28:43Z <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#6530 Answer by Mariano Suárez-Alvarez for Solvable subgroups of groups of polynomial automorphisms Mariano Suárez-Alvarez 2009-11-23T04:28:43Z 2009-11-23T04:28:43Z <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>