Abstract
Let ℂ¦x¦ be the ring of formal power series in one indeterminate x over ℂ, denote by Γ the group of invertible series in ℂ¦x¦, and by EΓ the set of all iterative roots of x in Γ. Then we will show that EΓ is neither a subgroup of Γ nor a family of commuting series. We describe all subgroups of Γ lying in EΓ, they are abelian and isomorphic to subgroups of the group E of complex roots of unity. Furthermore we determine the maximal subgroups of Γ in E{Γ} and use them to investigate how the subgroups in E I are related.
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János Aczél zum 70. Geburtstag in Dankbarkeit und Freundschaft gewidmet.
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Reich, L. Über Gruppen Von Iterativen Wurzeln Der Formalen Potenzreihe F(x) = x. Results. Math. 26, 366–371 (1994). https://doi.org/10.1007/BF03323061
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DOI: https://doi.org/10.1007/BF03323061