{"paper":{"title":"Generating the Mobius group with involution conjugacy classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ara Basmajian, Karan Puri","submitted_at":"2010-12-28T21:44:53Z","abstract_excerpt":"A {\\it $k$-involution} is an involution with a fixed point set of codimension $k$. The conjugacy class of such an involution, denoted $S_k$, generates $\\text{M\\\"ob}(n)$-the the group of isometries of hyperbolic $n$-space-if $k$ is odd, and its orientation preserving subgroup if $k$ is even. In this paper, we supply effective lower and upper bounds for the $S_k$ word length of $\\text{M\\\"ob}(n)$ if $k$ is odd, and the $S_k$ word length of $\\text{M\\\"ob}^+(n)$, if $k$ is even. As a consequence, for a fixed codimension $k$ the length of $\\text{M\\\"ob}^{+}(n)$ with respect to $S_k$, $k$ even, grows l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5845","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"}