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Normal subgroup generated by a plane polynomial automorphism

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Abstract

We study the normal subgroup 〈f〉 N 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 〈f〉 N = G. On the other hand, if f is a sufficiently generic element of even length at least 14, we prove that 〈f〉 N ≠ G.

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Authors and Affiliations

  1. Laboratoire MIA, Université de La Rochelle, Avenue M. Crépeau, 17042, La Rochelle cedex, France

    Jean-Philippe Furter

  2. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

    Stéphane Lamy

Authors
  1. Jean-Philippe Furter
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  2. Stéphane Lamy
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Correspondence to Jean-Philippe Furter.

Additional information

On leave from the Institut Camille Jordan, Université Lyon 1, France.

The second author was partially supported by an IEF Marie Curie Fellowship.

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Furter, JP., Lamy, S. Normal subgroup generated by a plane polynomial automorphism. Transformation Groups 15, 577–610 (2010). https://doi.org/10.1007/s00031-010-9095-4

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  • DOI: https://doi.org/10.1007/s00031-010-9095-4

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