{"paper":{"title":"Uniqueness of roots up to conjugacy for some affine and finite type Artin groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Eon-Kyung Lee, Sang-Jin Lee","submitted_at":"2007-11-01T10:58:44Z","abstract_excerpt":"Let $G$ be one of the Artin groups of finite type ${\\mathbf B}_n={\\mathbf C}_n$, and affine type $\\tilde{\\mathbf A}_{n-1}$ and $\\tilde{\\mathbf C}_{n-1}$. In this paper, we show that if $\\alpha$ and $\\beta$ are elements of $G$ such that $\\alpha^k=\\beta^k$ for some nonzero integer $k$, then $\\alpha$ and $\\beta$ are conjugate in $G$. For the Artin group of type $\\mathbf A_n$, this was recently proved by J. Gonz\\'alez-Meneses.\n  In fact, we prove a stronger theorem, from which the above result follows easily by using descriptions of those Artin groups as subgroups of the braid group on $n+1$ stran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0091","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"}