2016/04/26 by Serge Bouc, Bouc, Serge
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Immunology and Microbiology · Mathematics · #Algebraic Topology (math.AT) #Category Theory (math.CT) #Chromosomal and Genetic Variations #FOS: Mathematics #Genomic variations and chromosomal abnormalities #Group Theory (math.GR) #Immunodeficiency and Autoimmune Disorders #K-Theory and Homology (math.KT) #math.AT #math.CT #math.GR #math.KT
paper · pdf · doi:10.48550/arxiv.1604.07703
arxiv created 2016/04/26 · openalex publication_date 2016/04/26 · arxiv updated 2016/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p be an odd prime number. In this paper, we show that the genome Γ(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 K1(ℚP). It follows that the assignment P → Γ(P) is a p-biset functor. We give an explicit formula for the action of bisets on Γ, in terms of generalized transfers associated to left free bisets. Finally, we show that Γ is a rational p-biset functor, i.e. that Γ factors through the Roquette category of finite p-groups.