Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 310-01. Rational homology and Quillen's conjecture
Manuscript map · lines 8505–8514
OpenAI@2026-10-07#rem:oai-p-310-01
Authors: OpenAI. Family 310.
Title: Rational homology and Quillen's conjecture.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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