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Quillen's conjecture in rational homology
Proves the rational-homology form of Quillen's conjecture for every finite group and every prime. If the largest normal p-subgroup of G is trivial, the poset of nontrivial elementary abelian p-subgroups has nonzero augmented reduced rational homology and is therefore not contractible.
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Rational homology and Quillen's conjecture
Sep 24, 2026·paper.pdf
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 , 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.