On Stoll’s criterion for the maximality of quadratic arboreal Galois representations

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Abstract

We show that for a quadratic polynomial f(x) = x2- c, where c= (8 k+ 2) (8 k+ 3) or c= (4 k+ 1) (4 k+ 2) + 1 with k∈ N∪ { 0 } , the Galois group of the splitting field of each iterate fn of f is isomorphic to the automorphism group of a complete binary rooted tree of height n.

Original languageEnglish
JournalArchiv der Mathematik
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Arboreal Galois representation
  • Automorphism group
  • Wreath product

ASJC Scopus subject areas

  • Mathematics(all)

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