{"paper":{"title":"Ideals and Solvability in Skew Braces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"G\\\"ulin Ercan, Marco Damele","submitted_at":"2026-07-22T09:30:15Z","abstract_excerpt":"We investigate how nilpotency assumptions on the multiplicative group of a finite skew brace constrain its ideal structure and solvability. Our first main result shows that, if \\(B=(B,+,\\cdot)\\) is finite and \\((B,\\cdot)\\) is nilpotent, then the additive Fitting subgroup \\(F(B,+)\\) is a non-zero ideal of \\(B\\). As consequences, every finite simple skew brace with nilpotent multiplicative group is isomorphic to \\(\\Triv(C_p)\\) for some prime \\(p\\), and every such skew brace admits an ideal of prime index. In particular, \\[ B*B\\neq B \\qquad\\text{and}\\qquad \\partial(B) \\neq B. \\] We also show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19955","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/2607.19955/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"}