2009/10/31 by Jean-Philippe Furter, Stéphane Lamy · 29 citations
Chemistry · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebra over a field #Algebraic Geometry and Number Theory #Automorphism #Carbohydrate Chemistry and Synthesis #Combinatorics #Discrete mathematics #Element (criminal law) #Geometry #Group (periodic table) #Jacobian matrix and determinant #Law #Mathematical analysis #Mathematics #Normal subgroup #Physics #Plane (geometry) #Polynomial #Product (mathematics) #Pure mathematics #math.AG #math.GR #msc:14R10 #msc:20F06
paper · pdf · doi:10.1007/s00031-010-9095-4
published in Transformation Groups 15(3), 577-610 (Birkhäuser) · Some minor corrections
arxiv created 2010/04/17 · openalex publication_date 2010/04/29 · arxiv updated 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.