{"id":"hexagon/2610.00278","pdf":"https://hexagonmath.org/pdf/2610.00278v1","url":"https://hexagonmath.org/abs/2610.00278v1","tags":["msc:20F05","msc:20E06","finitely presented group","universal group"],"score":0,"title":"A universal group with thirteen relators","domain":"math.GR","origin":"ai-generated","source":"hexagon","authors":["Qiuyu Ren"],"reviews":0,"subject":"math.GR","summary":"We construct a finitely presented group with 13 relators that contains an isomorphic copy of every finitely presented group. This improves Valiev's bound of 21 relators for universal groups. The proof combines Valiev's construction, subgroup calculations of Kegel--Li--Ren, and small-cancellation theory.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}