Mathematical Proceedings of the Cambridge Philosophical Society

The centric p-radical complex and a related p-local geometry

a1 Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan.


We shall introduce a p-local geometry Δp(G) for the pair (G, p) of a finite group G and a prime divisor p of the order of G, which is constructed by ‘maximal parabolic like’ subgroups of G. Under the natural hypothesis, Δp(G) behaves very much like the building associated with a group of Lie type in characteristic p. We shall also show that, under some hypothesis, Δp(G) is homotopy equivalent to the subgroup complex [script B]cenp(G) which is a more essential part of the p-radical complex [script B]p(G). Some of the p-local sporadic geometries can be understood well in our system.

(Received January 30 2001)
(Revised May 15 2001)


1 Partially supported by a grant from the Japan Society for the Promotion of Science.