{"paper":{"title":"A Finite Skew Brace with Perfect Additive Group and Almost Simple Multiplicative Group","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Maria Ferrara, Massimiliano Di Matteo","submitted_at":"2026-07-15T17:31:40Z","abstract_excerpt":"We construct a finite skew brace whose additive group is perfect and whose multiplicative group is non-perfect and almost simple. This gives an affirmative answer to Problem 20.109 in the twenty-first edition of the Kourovka Notebook. The additive and multiplicative groups of our example are \\[\n  \\PSU_5(64)\\times A_5\n  \\quad\\text{and}\\quad\n  \\Aut(\\PSU_5(64)), \\] respectively. The construction combines a skew brace with additive group \\(A_5\\) and multiplicative group \\((C_5\\rtimes C_4)\\times C_3\\), the splitting of the automorphism extension of \\(\\PSU_5(64)\\), and a semidirect product of skew b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14059","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/2607.14059/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"}