Transformation Groups

, Volume 15, Issue 3, pp 577–610 | Cite as

Normal subgroup generated by a plane polynomial automorphism

Article

Abstract

We study the normal subgroup 〈fN generated by an element f ≠ id in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On the one hand, if f has length at most 8 relative to the classical amalgamated product structure of G, we prove that 〈fN = G. On the other hand, if f is a sufficiently generic element of even length at least 14, we prove that 〈fNG.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Laboratoire MIAUniversité de La RochelleLa Rochelle cedexFrance
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUnited Kingdom

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