Finite index theorems for iterated Galois groups of preperiodic points for unicritical polynomials

Abstract

Let K be a number field and let f(x) = x^q + c where q is a prime power, c is in K, and f is not post-critically finite. We show that for any strictly preperiodic b in K, the iterated Galois group at b with respect to f has finite index in the generic iterated Galois group for f.

15 pages. arXiv admin note: substantial text overlap with arXiv:1810.00990