{"paper":{"title":"Artin groups of type B and D","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"J. Crisp, L. Paris","submitted_at":"2002-10-29T09:47:23Z","abstract_excerpt":"We show that each of the Artin groups of type $B_n$ and $D_n$ can be presented as a semidirect product $F \\rtimes {\\cal B}_n$, where $F$ is a free group and ${\\cal B}_n$ is the $n$-string braid group. We explain how these semidirect product structures arise quite naturally from fibrations, and observe that, in each case, the action of the braid group ${\\cal B}_n$ on the free group $F$ is classical. We prove that, for each of the semidirect products, the group of automorphisms which leave invariant the normal subgroup $F$ is small: namely, ${\\rm Out}(A(B_n),F)$ has order 2, and ${\\rm Out}(A(D_n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210438","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0210438/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}