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arXiv · 2508.00266

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

Minsik Han·Thomas J. Tucker
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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.

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Minsik Han, Thomas J. Tucker. 2025-08-01. Finite index theorems for iterated Galois groups of preperiodic points for unicritical polynomials. https://arxiv.org/abs/2508.00266

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