{"paper":{"title":"Pro-Hall $R$-groups and groups discriminated by the free pro-$p$ group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ilya Kazachkov, Montserrat Casals-Ruiz, Vladimir Remeslennikov","submitted_at":"2018-03-01T16:08:59Z","abstract_excerpt":"In this note we introduce pro-Hall $R$-groups as inverse limits of Hall $R$-groups and show that for the binomial closure $S^{bin}$ of any ring $S$ discriminated by $\\mathbb{Z}_p$, the free pro-Hall $S^{bin}$-group $\\mathbb{F}(A,S^{bin})$ is fully residually free pro-$p$. Furthermore, we prove that any finite set of elements in $\\mathbb{F}(A,S^{bin})$ defines a pro-$p$ subgroup and so an irreducible coordinate group over the free pro-$p$ group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00478","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"}