{"paper":{"title":"Quotient groups of IA-automorphisms of a free group of rank 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"A.I. Papistas, H. Sevaslidou, V. Metaftsis","submitted_at":"2017-01-10T08:48:28Z","abstract_excerpt":"We prove that, for any positive integer $c$, the quotient group $\\gamma_{c}(M_{3})/\\gamma_{c+1}(M_{3})$ of the lower central series of the McCool group $M_{3}$ is isomorphic to two copies of the quotient group $\\gamma_{c}(F_{3})/\\gamma_{c+1}(F_{3})$ of the lower central series of a free group $F_{3}$ of rank $3$ as $\\mathbb{Z}$-modules. Furthermore, we give a necessary and sufficient condition whether the associated graded Lie algebra ${\\rm gr}(M_{3})$ of $M_3$ is naturally embedded into the Johnson Lie algebra ${\\cal L}({\\rm IA}(F_{3}))$ of the IA-automorphisms of $F_{3}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02478","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"}