{"paper":{"title":"Almost-crystallographic groups as quotients of Artin braid groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"CNRS, Daciberg Lima Gon\\c{c}alves (IME, John Guaschi (LMNO, NU), Oscar Ocampo (UFBA), UNICAEN, USP)","submitted_at":"2018-05-29T12:04:39Z","abstract_excerpt":"Let $n, k \\geq 3$. In this paper, we analyse the quotient group $B\\_n/\\Gamma\\_k(P\\_n)$ of the Artin braid group $B\\_n$ by the subgroup $\\Gamma\\_k(P\\_n)$ belonging to the lower central series of the Artin pure braid group $P\\_n$. We prove that it is an almost-crystallographic group. We then focus more specifically on the case $k=3$. If $n \\geq 5$, and if $\\tau \\in N$ is such that $gcd(\\tau, 6) = 1$, we show that $B\\_n/\\Gamma\\_3 (P\\_n)$ possesses torsion $\\tau$ if and only if $S\\_n$ does, and we prove that there is a one-to-one correspondence between the conjugacy classes of elements of order $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11376","kind":"arxiv","version":2},"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"}