Title: Cellularization of classifying spaces and fusion properties of finite groups

Authors: Ramon J. Flores, Jerome Scherer

AMS classification numbers: Primary 55P60, 20D200; Secondary 55R37, 55Q05

ArXiv submission number: math.AT/0501442

email: ramonj@mat.uab.es, jscherer@mat.uab.es

Abstract: One way to understand the mod p homotopy theory
of classifying spaces of finite groups is to compute their
B\Z/p-cellularization. In the easiest cases this is a
classifying space of a finite group (always a finite p-group).
If not, we show that it has infinitely many non-trivial
homotopy groups. Moreover they are either p-torsion free
or else infinitely many of them contain p-torsion. By means
of techniques related to fusion systems we exhibit concrete
examples where p-torsion appears.