{"id":"openai-math/Rational-homology-and-Quillens-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/Rational-homology-and-Quillens-conjecture-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Rational-homology-and-Quillens-conjecture-September-24-2026","tags":["group-theory","algebraic-topology","finite-groups"],"score":0,"title":"Rational homology and Quillen's conjecture","domain":"Topology","family":"310","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"We prove Quillen's conjecture for all finite groups and all primes. More precisely, if a finite group G has trivial largest normal p -subgroup $`O_p(G)`$, then the poset of nontrivial elementary abelian p -subgroups of G has nonzero augmented reduced rational homology. This establishes the stronger rational-homology form of the conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Quillen's conjecture in rational homology"}