{"paper":{"title":"Twisted conjugacy and quasi-isometry invariance for generalized solvable Baumslag-Solitar groups","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Jennifer Taback, Peter Wong","submitted_at":"2006-01-12T02:46:37Z","abstract_excerpt":"We say that a group has property $R_{\\infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\\infty}$. We define a solvable generalization $\\Gamma(S)$ of these groups which we show to have property $R_{\\infty}$. We then show that property $R_{\\infty}$ is geometric for these groups, that is, any group quasi-isometric to $\\Gamma(S)$ has property $R_{\\infty}$ as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601271","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"}