{"paper":{"title":"Totally disconnected groups from Baumslag-Solitar groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"George Willis, Murray Elder","submitted_at":"2013-01-21T07:56:33Z","abstract_excerpt":"For each Baumslag-Solitar group BS(m,n) (m,n nonzero integers), a totally disconnected, locally compact group, G_{m,n}, is constructed so that BS(m,n) is identified with a dense subgroup of G_{m,n}. The scale function on G_{m,n}, a structural invariant for the topological group, is seen to distinguish the parameters m and n to the extent that the set of scale values is {(lcm(m,n)/|m|)^{\\rho}, (lcm(m,n)/|n|)^{\\rho} | \\rho\\in N}. It is also shown that G_{m,n} has flat rank 1 when |m|\\neq |n| and 0 otherwise, and that G_{m,n} has a compact, open subgroup isomorphic to the product {(Z_p,+) | p is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4775","kind":"arxiv","version":3},"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"}