{"paper":{"title":"The lower $p$-central series of a free profinite group and the shuffle algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.NT","authors_text":"Ido Efrat","submitted_at":"2018-08-16T06:13:37Z","abstract_excerpt":"For a prime number $p$ and a free profinite group $S$ on the basis $X$, let $S^{(n,p)}$, $n=1,2,\\ldots$ be the lower $p$-central filtration of $S$. For $p>n$, we give a combinatorial description of $H^2(S/S^{(n,p)},\\mathbb{Z}/p)$ in terms of the Shuffle algebra on $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05354","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"}