Induced resolutions and grothendieck groups of polycyclic-by-finite-groups

Kenneth A. Brown, James Howie, Martin Lorenz

Research output: Contribution to journalArticle

Abstract

Let G{cyrillic} be a polycyclic-by-finite group, R a commutative Noetherian ring, G0(RG{cyrillic}) the Grothendieck group of finitely generated RG{cyrillic}-modules, and G0(RG{cyrillic},F) the subgroup generated by the classes of modules induced from finite subgroups of G{cyrillic}. It is expected that G0(RG{cyrillic})=G0(RG{cyrillic},F). As partial evidence for this, we show that G0(RG{cyrillic}) G0(RG{cyrillic},F) is torsion, with an explicit bound for the exponent, in the case where G{cyrillic} is abelian-by-finite and R a regular Noetherian Hilbert ring of finite global dimension. © 1988.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Pure and Applied Algebra
Volume53
Issue number1-2
Publication statusPublished - Aug 1988

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