A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver
成果类型：
Article
署名作者：
Aschbacher, Michael; Chermak, Andrew
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2010.171.881
发表日期：
2010
页码：
881-978
关键词：
摘要：
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(0) -> g(1) -> ... ) of 2-local finite groups, via a representation of a chain &* = (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 & exists in the category of 2-local groups, and that it is the 2-local group of the union of the chain &*. 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].