Corpus ID: 119591405

# Elements of Finite Order in the Group of Formal Power Series Under Composition

@article{Cohen2018ElementsOF,
title={Elements of Finite Order in the Group of Formal Power Series Under Composition},
author={Marshall M. Cohen},
journal={arXiv: Combinatorics},
year={2018}
}
We consider formal power series $f(z) = \omega z + a_2z^2 + \ldots \ (\omega \neq 0)$, with coefficients in a field of characteristic $0$. These form a group under the operation of composition (= substitution). We prove (Theorem 1) that every element $f(z)$ of finite order is conjugate to its linear term $\ell_\omega(z) = \omega z$, and we characterize those elements which conjugate $f(z)$ to $\omega z$. Then we investigate the construction of elements of order $n$ and prove (Theorem 2) that… Expand
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