Results in Mathematics

, Volume 26, Issue 3–4, pp 366–371 | Cite as

Über Gruppen Von Iterativen Wurzeln Der Formalen Potenzreihe F(x) = x

  • Ludwig Reich


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.

1991 Mathematics Subject Classsification

39 B 12 13 F 25 

Keywords and phrases

Iterative roots of formal power series families of commuting formal series 


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Copyright information

© Birkhäuser Verlag, Basel 1994

Authors and Affiliations

  • Ludwig Reich
    • 1
  1. 1.Institut für MathematikUniversität GrazGrazAustria

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