For every PCF polynomial, the arboreal Galois image is contained in a newly defined sign-kernel overgroup of the tree automorphism group; for a new cubic example the image is exactly E^2_n(3).
Benedetto, Jennifer Cain, Gregory Carroll, and Lily Fang
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Overgroups of the arboreal representation of PCF polynomial
For every PCF polynomial, the arboreal Galois image is contained in a newly defined sign-kernel overgroup of the tree automorphism group; for a new cubic example the image is exactly E^2_n(3).