A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver

作者：Aschbacher Michael^*; Chermak Andrew

来源：Annals of Mathematics, 2010, 171(2): 881-978.

DOI：10.4007/annals.2010.171.881

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].

• 出版日期2010-3