A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver
A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver
复制标题
Levi 和 Oliver 构建的 $2$ 局部有限群族的群论方法
DOI：
10.4007/annals.2010.171.881
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发表时间：
2010
影响因子：
4.9
通讯作者：
A. Chermak
中科院分区：
文献类型：
--
作者：
M. Aschbacher;A. Chermak
我们将p-局部有限群的概念（在[BL 03]中定义）扩展到p-局部群的概念。我们定义态射的p-局部群，从而获得一个类别，我们介绍的概念表示的p-局部群通过信号函子与群体。我们构造了一个链G =（G_0 → G_1 →.）通过链G^* =（G_0 → G_1 →...）G_n是Levi和奥利弗在[LO 02]中构造的2-局部有限群之一。我们证明了G的直极限G存在于2-局部群范畴中，并且它是链G^* 的并的2-局部群。证明了G的2-完全分类空间是Dwyer和Wilkerson的奇异2-紧群的分类空间B DI（4）[DW 93]。
We extend the notion of a p-local finite group (defined in [BLO03]) to the notion of a p-local group. We define morphisms of p-local groups, obtaining thereby a category, and we introduce the notion of a representation of a p-local group via signalizer functors associated with groups. We construct a chain G = (G_0 → G_1 → ...) of 2-local finite groups, via a representation of a chain G^* = (G_0 → G_1 → ...) of groups, such that G_0 is the 2-local finite group of the third Conway sporadic group Co_3, and for n > 0, G_n is one of the 2-local finite groups constructed by Levi and Oliver in [LO02]. We show that the direct limit G of G exists in the category of 2-local groups, and that it is the 2-local group of the union of the chain G^*. The 2-completed classifying space of G is shown to be the classifying space B DI(4) of the exotic 2-compact group of Dwyer and Wilkerson [DW93].