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

2020/10/09 by Wayne Peng, Peng, Wayne
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.04846

openalex publication_date 2020/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Prime Divisors of the Sequence W n +1 = 1 + W 1 … W n

Related

• Dynamical Belyi maps and arboreal Galois groups
• Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case
• Arboreal Galois groups of postcritically finite quadratic polynomials: The periodic case
• Overgroups of the arboreal representation of PCF polynomial
• Explicit Belyi maps over Q having almost simple primitive monodromy groups