Abstract
In this paper, we prove that a free nilpotent group of finite rank is transitive self-similar. In contrast, we prove that a free metabelian group of rank \(r \ge 2\) is not transitive self-similar.
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Alex C. Dantas was supported by FAPDF and FEMAT. Tulio M.G. Santos acknowledges support from the Brazilian scientific agency CAPES.
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Berlatto, A.A., Dantas, A.C. & Santos, T.M.G. Self-similarity of some soluble relatively free groups. Arch. Math. 120, 361–371 (2023). https://doi.org/10.1007/s00013-023-01834-5
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DOI: https://doi.org/10.1007/s00013-023-01834-5