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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In Rational homology and Quillen’s conjecture, 24 September 2026
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For every finite group G and every prime p, if \Op(G)=1, then
Here reduced homology is augmented, so that the empty poset has \widetilde H_{-1}(\varnothing;\Q)=\Q.
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Theorem 1.1
In Rational homology and Quillen’s conjecture, 24 September 2026