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.