论文标题
消除Quillen猜想中的组件
Eliminating components in Quillen's Conjecture
论文作者
论文摘要
我们概括了SEGEV的较早结果，该结果表明，在最小的反例中{\ em某些\/}的组件对Quillen的猜想必须接受外部自动形态。我们实际上表明{\ em every \/}组件必须接受外部自动形态。因此，我们将他对组件的限制性重分转换为消除分子：即排除任何不承认外部自动形态的组件。确实，我们表明，所承认的外部自动形态必须包括$ p $ outers：即，订单的外部自动形态可除以$ p $。这提供了更强大，更具体的消除：例如，如果$ p $是奇怪的，则消除了零星和交替的组件 - 从而减少了lie-type组件（并且通常强迫$ p $ - field类型）。对于$ p = 2 $，我们获得类似但限制性较小的结果。我们还提供了一些工具来帮助消除在最小反例中允许$ p $ outers的合适组件。
We generalize an earlier result of Segev, which shows that {\em some\/} component in a minimal counterexample to Quillen's conjecture must admit an outer automorphism. We show in fact that {\em every\/} component must admit an outer automorphism. Thus we transform his restriction-result on components to an elimination-result: namely one which excludes any component which does not admit an outer automorphism. Indeed we show that the outer automorphisms admitted must include $p$-outers: that is, outer automorphisms of order divisible by $p$. This gives stronger, concrete eliminations: for example if $p$ is odd, it eliminates sporadic and alternating components -- thus reducing to Lie-type components (and typically forcing $p$-outers of field type). For $p = 2$, we obtain similar but less restrictive results. We also provide some tools to help eliminate suitable components that do admit $p$-outers in a minimal counterexample.
