21.41 (2026)
OpenA group is said to be self-similar if it admits a faithful state-closed representation by automorphisms of a regular one-rooted $m$-tree for some $m$. Can a torsion-free finitely presented metabelian group which is self-similar contain a subgroup isomorphic to the restricted wreath product $H = \mathbb{Z} \wr \mathbb{Z}$?
It is known that $\mathbb{Z}\wr\mathbb{Z}$ itself is self-similar (A. C. Dantas, T. M. G. Santos, S. N. Sidki, J. Algebra, 567 (2021), 564–581).
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