Control of fixed points and existence and uniqueness of centric linking systems
Control of fixed points and existence and uniqueness of centric linking systems
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固定点的控制以及中心连接系统的存在性和唯一性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Lynd
中科院分区：
文献类型：
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作者：
G. Glauberman;J. Lynd
A. Chermak最近证明了有限p-群上的每个饱和融合系统都存在唯一的中心联结系统。B。奥利弗扩展了切尔马克的证明，证明了所有与中心连接系统的唯一存在相关的更高的上同调障碍群都消失了。这两个证明都间接假设了有限单群的分类。我们展示了如何去除这个假设，从而给出了关于有限群的p-完备分类空间的Martino-Priddy猜想的无分类证明。我们的主要工具是1971年的结果，第一作者控制不动点的p-本地子群。这一结果是直接适用于奇素数，我们展示了如何轻微的变化，它允许应用程序$$p=2$$p=2在罪犯的存在。
A. Chermak has recently proved that to each saturated fusion system over a finite p-group, there is a unique associated centric linking system. B. Oliver extended Chermak’s proof by showing that all the higher cohomological obstruction groups relevant to unique existence of centric linking systems vanish. Both proofs indirectly assume the classification of finite simple groups. We show how to remove this assumption, thereby giving a classification-free proof of the Martino–Priddy conjecture concerning the p-completed classifying spaces of finite groups. Our main tool is a 1971 result of the first author on control of fixed points by p-local subgroups. This result is directly applicable for odd primes, and we show how a slight variation of it allows applications for $$p=2$$p=2 in the presence of offenders.