{"paper":{"title":"Rank and deficiency gradients of generalised Thompson groups of type F","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dessislava Kochloukova","submitted_at":"2013-11-04T10:36:09Z","abstract_excerpt":"For an arbitrary sequence $(G_s)$ of subgroups of finite index in the generalised Thompson group $$F_{n, \\infty} = \\langle x_0, x_1, \\ldots, x_m, \\ldots \\mid x_i^{x_j} = x_{i+ n-1} \\hbox{ for } i > j \\geq 0 \\rangle$$ it is shown that $\\sup_{s \\geq 1} d(G_s) < \\infty$ and that the deficiency gradient of $F_{n, \\infty}$ with respect to $(G_s)$ is 0 provided $[G : G_s]$ tends to infinity. A higher dimensional analogue is considered for $n = 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0637","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"}