Given a fusion system \({\mathcal {F}}\) defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize \({\mathcal {F}}\). We study these models when \({\mathcal {F}}\) is a fusion system of a finite group G and prove a theorem which relates the cohomology of an infinite group model \(\pi \) to the cohomology of the group G. We show that for the groups GL(n, 2), where \(n\ge 5\), the cohomology of the infinite group obtained using the Robinson model is different than the cohomology of the fusion system. We also discuss the signalizer functors \(P\rightarrow \Theta (P)\) for infinite group models and obtain a long exact sequence for calculating the cohomology of a centric linking system with twisted coefficients.

中文翻译：

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实现融合系统的无穷群的同调

给定一个在p-群S上定义的融合系统\（{\ mathcal {F}} \}，存在由Leary和Stancu和Robinson构造的无限组模型，它们实现\（{\ mathcal {F}} \\ ）。当\（{\ mathcal {F}} \）是一个有限群G的融合系统时，我们研究了这些模型，并证明了一个定理，该定理将无限群模型\（\ pi \）的同调性与该组的同调性相关联摹。我们证明对于GL（n，2）组，其中\（n \ ge 5 \），使用Robinson模型获得的无限群的同调不同于融合系统的同调。我们还讨论了无限组模型的信号传递函子\（P \ rightarrow \ Theta（P）\），并获得了一个长的精确序列，用于计算具有扭曲系数的中心链接系统的同调性。