Galois group over \(\mathbb{Q}\) of some iterated polynomials

DOI10.1007/BF01197321zbMath0758.11045MaRDI QIDQ1203560

Michael Stoll

Publication date: 10 February 1993

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

Galois grouprecursioniterated polynomialswreath product of the 2- element group

Mathematics Subject Classification ID

Galois theory (11R32) Recurrences (11B37) Polynomials (irreducibility, etc.) (11R09)

Related Items (33)

Arboreal Galois representations ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ Iterates of generic polynomials and generic rational functions ⋮ The arithmetic basilica: a quadratic PCF arboreal Galois group ⋮ Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map ⋮ Squarefree doubly primitive divisors in dynamical sequences ⋮ \(ABC\) implies a Zsigmondy principle for ramification ⋮ A dynamical characterization for monogenity at every level of some infinite -towers ⋮ Eventually stable quadratic polynomials over \(\mathbb{Q}\) ⋮ Construction of semiabelian Galois extensions ⋮ Galois groups of some iterated polynomials over cyclotomic extensions ⋮ Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity ⋮ Julia Robinson numbers and arithmetical dynamic of quadratic polynomials ⋮ Galois groups and prime divisors in random quadratic sequences ⋮ Backward orbits of critical points ⋮ An iterative construction of irreducible polynomials reducible modulo every prime ⋮ Abelian extensions in dynamical Galois theory ⋮ Irreducible polynomials in quadratic semigroups ⋮ Prime divisors in polynomial orbits over function fields ⋮ Galois uniformity in quadratic dynamics over \(k(t)\) ⋮ An equivariant isomorphism theorem for mod $\mathfrak {p}$ reductions of arboreal Galois representations ⋮ The set of stable primes for polynomial sequences with large Galois group ⋮ Finite index theorems for iterated Galois groups of cubic polynomials ⋮ Classifying Galois groups of small iterates via rational points ⋮ Iterated extensions and relative Lubin-Tate groups ⋮ On the irreducibility of the iterates of 𝑥ⁿ-𝑏 ⋮ Large arboreal Galois representations ⋮ On Stoll's criterion for the maximality of quadratic arboreal Galois representations ⋮ Dynamical height growth: left, right, and total orbits ⋮ Arboreal Galois representation for a certain type of quadratic polynomials ⋮ Odoni's conjecture for number fields ⋮ Current trends and open problems in arithmetic dynamics ⋮ The arithmetic of curves defined by iteration

Cites Work

• On the Galois groups of the iterates of x ² +1
• Realising wreath products of cyclic groups as Galois groups

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