### Abstract

Let G{cyrillic} be a polycyclic-by-finite group, R a commutative Noetherian ring, G_{0}(RG{cyrillic}) the Grothendieck group of finitely generated RG{cyrillic}-modules, and G_{0}(RG{cyrillic},F) the subgroup generated by the classes of modules induced from finite subgroups of G{cyrillic}. It is expected that G_{0}(RG{cyrillic})=G_{0}(RG{cyrillic},F). As partial evidence for this, we show that G_{0}(RG{cyrillic}) G_{0}(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 language | English |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Journal of Pure and Applied Algebra |

Volume | 53 |

Issue number | 1-2 |

Publication status | Published - Aug 1988 |

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## Cite this

Brown, K. A., Howie, J., & Lorenz, M. (1988). Induced resolutions and grothendieck groups of polycyclic-by-finite-groups.

*Journal of Pure and Applied Algebra*,*53*(1-2), 1-14.