Classification and decomposition of the Witt-Burnside ring and Burnside ring of a profinite group

摘要

Let G be a profinite group and q be an integer. In this paper, we investigate the structure of the Witt-Burnside ring functor W _G~q and the generalized Burnside ring functor B _G ~q, which are introduced in Oh ['q-deformation of Witt-Burnside rings', Math. Z. 257 (2007) 151-191]. More precisely, we prove a classification theorem as q ranges over the set of integers and a decomposition theorem over the category of binomial rings when G is given by a direct sum of finitely many finite groups whose orders are mutually relatively prime. Also connections between the ring of truncated Witt vectors and Witt-Burnside rings will be dealt with.