Remark: Family 310. 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.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.