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Derived length of solvable groups of local diffeomorphisms

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Abstract

Let \(G\) be a solvable subgroup of the group \({\mathrm{Diff}{{\,}_{}(\mathbb{C }^{n},0)}}\) of local complex analytic diffeomorphisms. Analogously as for groups of matrices we bound the solvable length of \(G\) by a function of \(n\). Moreover we provide the best possible bounds for connected, unipotent and nilpotent groups.

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Acknowledgments

We thank the referee for the helpful remarks.

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  1. Instituto de Matemática, UFF, Rua Mário Santos Braga S/N Valonguinho, Niterói, Rio de Janeiro, 24020-140, Brazil

    Mitchael Martelo & Javier Ribón

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  1. Mitchael Martelo
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  2. Javier Ribón
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Correspondence to Javier Ribón.

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Martelo, M., Ribón, J. Derived length of solvable groups of local diffeomorphisms. Math. Ann. 358, 701–728 (2014). https://doi.org/10.1007/s00208-013-0975-5

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  • DOI: https://doi.org/10.1007/s00208-013-0975-5

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