{"paper":{"title":"Normal elements of completed group algebras over ${\\rm SL}_3(\\mathbb{Z}_p) $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.NT","authors_text":"Dong Han, Feng Wei","submitted_at":"2018-02-08T00:06:14Z","abstract_excerpt":"Let $p$ be a prime integer and $\\mathbb{Z}_p$ be the ring of $p$-adic integers. By a purely computational approach we prove that each nonzero normal element of a completed group algebra over the special linear group ${\\rm SL}_3(\\mathbb{Z}_p)$ is a unit. This give a positive answer to an open question in \\cite{WeiBian2} and make up for an earlier mistake in \\cite{WeiBian1} simultaneously."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02676","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"}