{"paper":{"title":"A Bieberbach theorem for crystallographic group extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"John G. Ratcliffe, Steven T. Tschantz","submitted_at":"2016-07-12T20:19:52Z","abstract_excerpt":"In this paper we prove that for each dimension $n$ there are only finitely many isomorphism classes of pairs of groups $(\\Gamma,\\mathrm{N})$ such that $\\Gamma$ is an $n$-dimensional crystallographic group and $\\mathrm{N}$ is a normal subgroup of $\\Gamma$ such that $\\Gamma/\\mathrm{N}$ is a crystallographic group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03503","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"}