{"paper":{"title":"Exterior Algebra and an Extension of the Feng-Sun-Xiang Theorem in $p$-groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Lilu Zhao, Zhi-Wei Sun","submitted_at":"2026-06-29T16:12:56Z","abstract_excerpt":"Let $G$ be a finite group with $|G|=p^m$ where $p$ is a prime and $m$ is a positive integer. Let $k<p$. Let $a_1,\\ldots,a_k\\in G$ be pairwise distinct and let $b_1,\\ldots,b_k\\in G$. Then there exists a permutation $\\sigma$ on $1,\\ldots,k$ such that $a_1b_{\\sigma(1)},\\ldots,a_kb_{\\sigma(k)}$ are pairwise distinct. This extends a theorem of Feng, Sun and Xiang, who proved that the conclusion holds in abelian $p$-groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30506","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30506/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"}