{"paper":{"title":"Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Patrick Dehornoy (LMNO)","submitted_at":"2016-06-29T08:07:54Z","abstract_excerpt":"We describe a new approach to the Word Problem for Artin-Tits groups and, more generally, for the enveloping group U(M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite system R(M) that extends free reduction for free groups. Here we show that, if M satisfies what we call the 3-Ore condition about common multiples, what corresponds to type FC in the case of Artin-Tits monoids, then the system R(M) is convergent. Under this assumption, we obtain a unique representation result for the elements of U(M), extending Ore's theorem for groups of f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08991","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"}