Centric linking systems of locally finite groups

Abstract

These notes are defining the notion of centric linking system for a locally finite group. If a locally finite group G has countable Sylow p-subgroups, we prove that, with a finiteness condition on the set of intersections of Sylow p-subgroups, the p-completion of its classifying space is homotopy equivalent to the p-completion of the nerve of its centric linking system.