{"id":"openai-math/The-Kervaire-Theorem-for-Groups","pdf":"https://github.com/openai/math/blob/main/preprints/The-Kervaire-Theorem-for-Groups-September-24-2026/The-Kervaire-Theorem-for-Groups-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Kervaire-Theorem-for-Groups-September-24-2026","tags":["group-theory","kervaire-conjecture","free-products","combinatorial-group-theory"],"score":0,"title":"The Kervaire theorem for groups","domain":"Group theory","family":"256","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We prove that no free product of a nontrivial group with an infinite cyclic group is normally generated by one element. This resolves the Kervaire conjecture positively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Nonsingular systems of equations over arbitrary groups"}