Normal subgroup generated by a plane polynomial automorphism

Jean-Philippe Furter, Stéphane Lamy

Published 2009-10-08, updated 2010-04-17Version 2

We study the normal subgroup <f> generated by a non trivial element f in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On one hand if f has length at most 8 relatively to the classical amalgamated product structure of G, we prove that <f> = G. On the other hand if f is a sufficiently generic element of even length at least 14, we prove that <f> is a proper subgroup of G.