论文标题
外来融合系统的刺穿组
Punctured groups for exotic fusion systems
论文作者
论文摘要
Oliver和Ventura的运输系统以及Chermak的地区是一类代数结构，它们对有限群体的$ P $ - 局部结构进行了建模。除了有限群体的运输者类别和地点外，重要的例子包括饱和融合系统的中心，准和次级链接系统。但是，这些示例通常在Sylow组的子组的完整集合中均未定义。我们在这里研究了刺穿的组，转运者系统的缩写或在收集有限$ p $ group的非身份亚组的地方。作为刺穿群体的存在的应用，我们表明，对融合系统的中心集合中的亚组同源性分解是敏锐的。我们还证明了针对穿刺组的信号器函数定理，并使用它证明了Prime $ 2 $的最小的Benson-Solomon Exotic Fusion System具有刺穿的组，而其他人则没有。至于Odd Primes $ p $的异国情调融合系统，我们调查了几个类，发现在几乎所有情况下，次级链接系统是该系统的刺穿组，或者该系统没有刺破的组，因为某些订单$ p $的标准级是异国情调的。最后，我们将限制在订单$ p $ - 订单$ p^3 $的某些融合系统的插入式链接系统中进行分类。
The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the $p$-local structures of finite groups. Other than the transporter categories and localities of finite groups, important examples include centric, quasicentric, and subcentric linking systems for saturated fusion systems. These examples are however not defined in general on the full collection of subgroups of the Sylow group. We study here punctured groups, a short name for transporter systems or localities on the collection of nonidentity subgroups of a finite $p$-group. As an application of the existence of a punctured group, we show that the subgroup homology decomposition on the centric collection is sharp for the fusion system. We also prove a Signalizer Functor Theorem for punctured groups and use it to show that the smallest Benson-Solomon exotic fusion system at the prime $2$ has a punctured group, while the others do not. As for exotic fusion systems at odd primes $p$, we survey several classes and find that in almost all cases, either the subcentric linking system is a punctured group for the system, or the system has no punctured group because the normalizer of some subgroup of order $p$ is exotic. Finally, we classify punctured groups restricting to the centric linking system for certain fusion systems on extraspecial $p$-groups of order $p^3$.
