{"paper":{"title":"Finite-state self-similar actions of nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ievgen Bondarenko, Rostyslav Kravchenko","submitted_at":"2011-05-25T09:10:34Z","abstract_excerpt":"Let $G$ be a finitely generated torsion-free nilpotent group and $\\phi:H\\rightarrow G$ be a surjective homomorphism from a subgroup $H<G$ of finite index with trivial $\\phi$-core. For every choice of coset representatives of $H$ in $G$ there is a faithful self-similar action of the group $G$ associated with $(G,\\phi)$. We are interested in what cases all these actions are finite-state and in what cases there exists a finite-state self-similar action for $(G,\\phi)$. These two properties are characterized in terms of the Jordan normal form of the corresponding automorphism $\\widehat{\\phi}$ of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4969","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}