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.