{"paper":{"title":"Permutations that Destroy Arithmetic Progressions in Elementary $p$-Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.NT","authors_text":"Ashvin Swaminathan, Noam D. Elkies","submitted_at":"2016-01-27T20:47:56Z","abstract_excerpt":"Given an abelian group $G$, it is natural to ask whether there exists a permutation $\\pi$ of $G$ that \"destroys\" all nontrivial 3-term arithmetic progressions (APs), in the sense that $\\pi(b) - \\pi(a) \\neq \\pi(c) - \\pi(b)$ for every ordered triple $(a,b,c) \\in G^3$ satisfying $b-a = c-b \\neq 0$. This question was resolved for infinite groups $G$ by Hegarty, who showed that there exists an AP-destroying permutation of $G$ if and only if $G/\\Omega_2(G)$ has the same cardinality as $G$, where $\\Omega_2(G)$ denotes the subgroup of all elements in $G$ whose order divides $2$. In the case when $G$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07541","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":""},"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"}