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Normal subgroup generated by a plane polynomial automorphism

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Furter, Jean-Philippe and Lamy, Stephane (2010) Normal subgroup generated by a plane polynomial automorphism. Transformation Groups, Vol.15 (No.3). pp. 577-610. doi:10.1007/s00031-010-9095-4

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Official URL: http://dx.doi.org/10.1007/s00031-010-9095-4

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Abstract

We study the normal subgroup < f >(N) generated by an element f not equal 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 1 4, we prove that < f >(N) not equal G.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Transformation Groups
Publisher: Birkhaeuser Boston
ISSN: 1083-4362
Official Date: September 2010
Dates:
DateEvent
September 2010Published
Volume: Vol.15
Number: No.3
Number of Pages: 34
Page Range: pp. 577-610
DOI: 10.1007/s00031-010-9095-4
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: IEF

Data sourced from Thomson Reuters' Web of Knowledge

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