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arXiv · 2204.13055

Some results on Quillen's Conjecture via equivalent-poset techniques

Kevin I. Piterman·Stephen D. Smith
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Abstract

We extend the Main Theorem of Aschbacher and Smith on Quillen's Conjecture from $p>5$ to the remaining odd primes $p = 3,5$. In the process, we develop further combinatorial and homotopical methods for studying the poset of nontrivial elementary abelian $p$-subgroups of a finite group. The techniques lead to a number of further results on the Conjecture, often reducing dependence on the CFSG; in particular, we also provide some partial results toward the case of $p=2$.

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Kevin I. Piterman, Stephen D. Smith. 2022-04-27. Some results on Quillen's Conjecture via equivalent-poset techniques. https://arxiv.org/abs/2204.13055

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