Arboreal Galois Groups of Postcritically Finite Quadratic Polynomials: the Strictly Preperiodic Case

In Benedetto et al. (2025, J. Lond. Math. Soc., 112, Article no. e70257), we provided an explicit description of the arboreal Galois group of the postcritically finite polynomial $f(z) = z<^>2 +c$ in the special case when the critical point $0$ is periodic under the action of $f(z)$ . In the current article, we complete the picture for all postcritically finite polynomials by addressing the cases when $0$ is strictly preperiodic for the polynomial $f(z)$ .