Title :  Biset functors and genetic sections for $p$-groups

Author : Serge Bouc

Abstract : In this note I show that if $F$ is a biset functor
defined over finite $p$-groups, then for each finite
$p$-group $P$, there is a direct summand of $F(P)$
admitting a natural direct sum decomposition indexed
by the irreducible rational representations of $P$, or
equivalently, by the equivalence classes of origins in $P$,
or also by equivalence classes of genetic sections of $P$.
This leads to a description of the torsion part of the group
of relative syzygies in the Dade group of $P$, and to a
conjecture on the structure of the torsion part of
the whole Dade group of $P$.