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 language | English |
---|---|
Pages (from-to) | 133-140 |
Number of pages | 8 |
Journal | Archiv der Mathematik |
Volume | 117 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2021 Aug |
Keywords
- Arboreal Galois representation
- Automorphism group
- Wreath product
ASJC Scopus subject areas
- General Mathematics