{"paper":{"title":"FPn properties of generalized Houghton groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Heike Sach","submitted_at":"2016-07-23T14:18:41Z","abstract_excerpt":"This Thesis presents a 2-dimensional generalization of Houghtons' groups H_n. H_n is defined to be the group of all permutations p of a disjoint union of copies of the natural numbers N, with the property that each copy of N contains a cofinite subset on which p restricts to a translation. Our group G(n) is defined to be the group of all permutations p of a disjoint union of quadrants (i.e., copies of NxN) with the property that each quadrant contains a subquadrant on which p is a translation, while p restricted to the remaining set is piecewise isometric on a cofinite disjoint union of rays ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00933","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"}