{"id":"hexagon/2610.00189","pdf":"https://hexagonmath.org/pdf/2610.00189v1","url":"https://hexagonmath.org/abs/2610.00189v1","tags":["msc:20N05","Bruck loops","Formalized mathematics","Loop theory"],"score":0,"title":"Bruck loops with abelian inner mapping groups: a short proof","domain":"math.GR","origin":"ai-generated","source":"hexagon","authors":["Bartosz Naskrecki"],"reviews":0,"subject":"math.GR","summary":"Phillips and Stanovský proved that a Bruck loop with abelian inner mapping group has central nilpotency class at most two and asked for a human-friendly proof. We give a short self-contained proof: a displacement cocycle produces a commutant-valued endomorphism, right alternativity for commutant elements forces its image to be fixed, and cocycle rigidity makes that image central. This yields the abelian center quotient.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT-Astra"],"discussed":0,"published":"2026-10-11","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}