English

Normal subgroup generated by a plane polynomial automorphism

Group Theory 2018-04-24 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.0910.1616,
  title  = {Normal subgroup generated by a plane polynomial automorphism},
  author = {Jean-Philippe Furter and Stéphane Lamy},
  journal= {arXiv preprint arXiv:0910.1616},
  year   = {2018}
}

Comments

Some minor corrections

R2 v1 2026-06-21T13:56:02.479Z