{"paper":{"title":"On the first-order genus of wreath products and their central extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexei Miasnikov, Denis Osin, Olga Kharlampovich","submitted_at":"2026-03-16T19:53:44Z","abstract_excerpt":"We prove that groups of the form $\\mathbb Z^m {\\,\\rm wr\\,} \\mathbb Z^n$, where $m,n \\in \\mathbb N$, are regularly bi-interpretable with $\\mathbb Z$ and therefore are first-order rigid: every finitely generated group elementarily equivalent to $\\mathbb Z^m {\\,\\rm wr\\,} \\mathbb Z^n$ is isomorphic to $\\mathbb Z^m {\\,\\rm wr\\,} \\mathbb Z^n$. On the other hand, we show that $\\mathbb Z^2 {\\,\\rm wr\\,} \\mathbb Z$ admits $2^{\\aleph_0}$ elementarily equivalent, pairwise non-isomorphic central extensions with finite kernel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.15864","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.15864/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}