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arXiv · 2010.04846

A Unique Chief Series in the arboreal Galois Group of Belyi Maps

Wayne Peng
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Abstract

We give a complete description of the normal subgroups of arboreal Galois groups of Belyi maps. The normal groups form a unique chief series. We also carefully compute the discriminate of the iterate of a polynomial minus an algebraic number, which allows us to predict when a such discriminate is a perfect square in the base field or intermediate field for a postcritically finite polynomials (PCF). As a consequence we are able to find another PCF cubic polynomial that has the same arboreal Galois group as the one of Belyi maps.

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Wayne Peng. 2020-10-09. A Unique Chief Series in the arboreal Galois Group of Belyi Maps. https://arxiv.org/abs/2010.04846

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