{"paper":{"title":"Reidemeister classes in lamplighter type groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Evgenij Troitsky","submitted_at":"2017-11-26T12:00:22Z","abstract_excerpt":"We prove that for any automorphism $\\phi$ of the restricted wreath product $\\mathbb{Z}_2 \\mathrm{wr} \\mathbb{Z}^k$ and $\\mathbb{Z}_3 \\mathrm{wr} \\mathbb{Z}^{2d}$ the Reidemeister number $R(\\phi)$ is infinite, i.e. these groups have the property $R_\\infty$.\n  For $\\mathbb{Z}_3 \\mathrm{wr} \\mathbb{Z}^{2d+1}$ and $\\mathbb{Z}_p \\mathrm{wr} \\mathbb{Z}^k$, where $p>3$ is prime, we give examples of automorphisms with finite Reidemeister numbers. So these groups do not have the property $R_\\infty$.\n  For these groups and $\\mathbb{Z}_m \\mathrm{wr} \\mathbb{Z}$, where $m$ is relatively prime to $6$, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09371","kind":"arxiv","version":1},"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"}