Rational homology and Quillen's conjecture
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.
Cite
@misc{OAI:Rational-homology-and-Quillens-conjecture-September-24-2026,
author = {{OpenAI}},
title = {{Rational homology and Quillen's conjecture}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Rational-homology-and-Quillens-conjecture-September-24-2026/paper.pdf}{OAI:Rational-homology-and-Quillens-conjecture-September-24-2026}},
year = {2026}
}