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Classification and decomposition of the Witt–Burnside ring and Burnside ring of a profinite group
Author(s) -
Oh YoungTak
Publication year - 2012
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdr045
Subject(s) - mathematics , witt vector , profinite group , ring (chemistry) , functor , pure mathematics , prime (order theory) , group (periodic table) , discrete mathematics , combinatorics , algebra over a field , chemistry , organic chemistry
Let G be a profinite group and q be an integer. In this paper, we investigate the structure of the Witt–Burnside ring functor B q G 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.