Author : Fumihito Oda

Title  : The crossed Burnside ring, the Drinfel'd double,
and the Dade group of a $p$-group

Abstract :   Let $p$ be a prime number.
     This paper solves the question of the difference between the rank of
the crossed Burnside ring $B^c(P)$ of a finite $p$-group $P$
and of the rational representation ring $R_{{\mathbb{Q}}} (\mathscr{D}(P))$ of
the Drinfel'd double $\mathscr{D}(P)$ of the group algebra ${\mathbb{Q}} P.$
    The difference is represented by using the Dade groups
of certain subgroups of $P.$

Status : Preprint.