特征p下的分支与Quillen猜想
Components in characteristic $p$ and Quillen's conjecture
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中文总结 AI 辅助
该研究针对群论中的Quillen猜想，在温和归纳假设下证明含特征p李型单群分支且O_p(G)=1的群，其Quillen偏序集有非零有理同调，为p=2时的猜想研究提供关键依据。
中文摘要 AI 辅助
本文旨在证明，在温和的归纳假设下，若群G包含一个特征p下的李型单群分支且O_p(G)=1，则G在素数p处的Quillen偏序集具有非零有理同调。特别地，这表明此类分支不可能出现在Quillen猜想的极小反例中，该结果对仍未解决的素数p=2情形尤为重要。
英文摘要
The purpose of this paper is to show that, under mild inductive assumptions, if a group $G$ contains a component that is a simple group of Lie type in characteristic $p$ and $O_p(G) = 1$, then the Quillen poset of $G$ at $p$ has nonzero rational homology. In particular, this shows that such components cannot arise in a minimal counterexample to Quillen's conjecture. This result is of particular interest at the prime $p=2$, where the conjecture is still open.
