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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 ISSN 1083-4362.
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Official URL: http://dx.doi.org/10.1007/s00031-010-9095-4
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, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Transformation Groups | ||||
| Publisher: | Birkhaeuser Boston | ||||
| ISSN: | 1083-4362 | ||||
| Official Date: | September 2010 | ||||
| Dates: |
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| 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 |
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