HOMOTOPY EQUIVALENCES OF p-COMPLETED CLASSIFYING SPACES OF FINITE GROUPS 
By C. Broto, R. Levi and B. Oliver

AMS Classification: 55R35 

Address: 
Carles Broto, Departament de Mathematiques, Universitat 
Autonoma de Barcelona, E08193 Bellaterra, Spain 
Ran Levi, Department of Mathematical Sciences, University 
of Aberdeen, Aberdeen, AB24 3UE, Scotland 
Bob Oliver, LAGA, Institut Galilee, Av. J-B Clement,
 93439 Villetaneuse, France 


Abstract 
We study homotopy equivalences of $p$-completions of classifying spaces of 
finite groups.  To each finite group $G$ and each prime $p$, we associate a 
finite category $\bcallpc(G)$ with the following properties.  Two 
$p$-completed classifying spaces $BG\pcom$ and $BG'\pcom$ have the same 
homotopy type if and only if the associated categories $\bcallpc(G)$ and 
$\bcallpc(G')$ are equivalent.  And the topological group $Aut(BG\pcom)$ 
of self equivalences is determined by the self equivalences of the 
associated category $\bcallpc(G)$. 

Stage: Submitted, Preprint available.