Preprint: The group of endo-permutation modules

Authors:
Serge Bouc and Jacques Th\'evenaz

Addresses:
Serge Bouc UFR de Math\'ematiques, Universit\'e de Paris VII, 2 place
Jussieu, F--75251 Paris, France 

Jacques Th\'evenaz Institut de Math\'ematiques, Universit\'e de Lausanne,
 CH--1015 Lausanne, Switzerland 

Abstract:

	The group $D(P)$ of all endo-permutation modules for a finite
$p$-group $P$ is a finitely generated abelian group. We prove that its 
torsion-free rank is equal to the number of conjugacy classes of 
non-cyclic subgroups of $P$. We also obtain partial results on its 
torsion subgroup. 
	We determine next the structure of $\Q\otimes D(-)$ viewed as a 
functor, which turns out to be a simple functor $\sc S_{E,\Q}$, indexed 
by the elementary group $E$ of order $p^2$ and the trivial 
$\Out(E)$-module $\Q$. 
Finally we describe a rather strange exact sequence relating
$\Q\otimes D(P)$, $\Q\otimes B(P)$, and $\Q\otimes R(P)$, where 
$B(P)$ is the Burnside ring and $R(P)$ is the Grothendieck ring of 
$\Q P$-modules.