{"paper":{"title":"Random quotients of the modular group are rigid and essentially incompressible","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Paul Schupp","submitted_at":"2006-04-14T20:15:12Z","abstract_excerpt":"We show that for any positive integer $m\\ge 1$,\n  $m$-relator quotients of the modular group $M = PSL(2,\\mathbb{Z})$ generically satisfy a very strong Mostow-type \\emph{isomorphism rigidity}. We also prove that such quotients are generically \"essentially incompressible\". By this we mean that their \"absolute $T$-invariant\", measuring the smallest size of any possible finite presentation of the group, is bounded below by a function which is almost linear in terms of the length of the given presentation. We compute the precise asymptotics of the number $I_m(n)$ of \\emph{isomorphism types} of $m$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604343","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"}