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arXiv · 2505.19649

A just-infinite iterated monodromy group without the congruence subgroup property

Santiago Radi
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Abstract

We prove that the iterated monodromy group of the polynomial $z^2+i$ is just-infinite, regular branch and does not have the congruence subgroup property. This yields the first example of an iterated monodromy group of a polynomial with these properties. Additional information is provided about the congruence kernel, rigid kernel and branch kernel of this group.

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Santiago Radi. 2025-05-26. A just-infinite iterated monodromy group without the congruence subgroup property. https://doi.org/10.1515/jgth-2025-0126

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