{"paper":{"title":"Z-Structures on Product Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Carrie J. Tirel","submitted_at":"2010-10-02T01:27:13Z","abstract_excerpt":"A Z-structure on a group G, defined by M. Bestvina, is a pair (\\hat{X}, Z) of spaces such that \\hat{X} is a compact ER, Z is a Z-set in \\hat{X}, G acts properly and cocompactly on X=\\hat{X}\\Z, and the collection of translates of any compact set in X forms a null sequence in \\hat{X}. It is natural to ask whether a given group admits a Z-structure. In this paper, we will show that if two groups each admit a Z-structure, then so do their free and direct products."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0284","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"}