{"paper":{"title":"Sylow theory and the nilpotency class of left nilpotent skew braces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\c{S}\\\"ukran G\\\"ul, G\\\"ulin Ercan, \\.Ismail \\c{S}. G\\\"ulo\\u{g}lu, M. Yasir K{\\i}zmaz","submitted_at":"2026-06-24T11:01:30Z","abstract_excerpt":"Let $X$ be a finite left nilpotent skew brace and let $p$ be a prime dividing $|X|$. We show that every Sylow $p$-subgroup of the multiplicative group $(X,\\cdot)$ is a Sylow $p$-subbrace of $X$, and that every $p$-subbrace of $X$ is contained in some Sylow $p$-subbrace. This extends a recent result of Caranti, Del Corso, Di Matteo, Ferrara, and Trombetti by removing the solvability assumption. As an application, we obtain an upper bound for the left nilpotency class of $X$ in terms of the left nilpotency classes of its Sylow $p$-subbraces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25691","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/2606.25691/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"}