We construct a new example of a group of non-uniform exponential growth, which is an extension of an abelian group by the Grigorchuk-Erschler group. This group has Cayley graphs locally isomorphic to the Cayley graphs of the iterated monodromy group of $z^2+i$. Both groups belong to an interesting Cantor set of marked groups with dense isomorphism classes, related to a post-critically finite rational map of $PC^2$.

Lecture #12584

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