Title : A sectional characterization of the Dade group
Authors : Serge Bouc and Jacques Thévenaz
Abstract :
Let $k$ be a field of characteristic $p$ , let $P$ be a finite $p$-
group, where $p$ is an odd prime, and let $D(P)$ be the Dade group of 
endo-permutation $kP$-modules. It is known that $D(P)$ is detected 
via deflation--restriction by the family of all sections of~$P$ which 
are elementary abelian of rank~$\leq2$.
In this paper, we improve this result by characterizing $D(P)$ as the 
limit (with respect to deflation--restriction maps and conjugation 
maps) of all groups $D(T/S)$ where $T/S$ runs through all sections of~$P$ which are either elementary abelian of rank~$\leq3$ or 
extraspecial of order~$p^3$ and exponent~$p$.