K-theory, genotypes, and biset functors
K-theory, genotypes, and biset functors
Let p be an odd prime number. In this paper, we show that the genome $\Gamma(P)$ of a finite $p$-group $P$, defined as the direct product of the genotypes of all rational irreducible representations of $P$, can be recovered from the first group of $K$-theory $K_1(\mathbb{Q}P)$. It follows that the …