{"paper":{"title":"Reidemeister classes in some weakly branch groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Evgenij Troitsky","submitted_at":"2018-04-10T19:26:55Z","abstract_excerpt":"We prove that a saturated weakly branch group $G$ has the property $R_\\infty$ (any automorphism $\\phi:G\\to G$ has infinite Reidemeister number) in each of the following cases:\n  1) any element of $Out(G)$ has finite order;\n  2) for any $\\phi$ the number of orbits on levels of the tree automorphism $t$ inducing $\\phi$ is uniformly bounded and $G$ is weakly stabilizer transitive;\n  3) $G$ is finitely generated, prime-branching, and weakly stabilizer transitive with some non-abelian stabilizers (with no restrictions on automorphisms).\n  Some related facts and generalizations are proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03695","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"}