Non-finiteness results for Nil-groups

Grunewald, Joachim

doi:10.2140/agt.2007.7.1979

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Non-finiteness results for Nil-groups

Joachim Grunewald

Algebraic & Geometric Topology 7 (2007) 1979–1986

DOI: 10.2140/agt.2007.7.1979

Abstract

Generalizing an idea of Farrell we prove that for a ring $Λ$ and a ring automorphism $α$ of finite order the groups ${Nil}_{0} (Λ; α)$ and all of its $p$ –primary subgroups are either trivial or not finitely generated as an abelian group. We also prove that if $β$ and $γ$ are ring automorphisms such that $β \circ γ$ is of finite order then ${Nil}_{0} (Λ; Λ_{β}, Λ_{γ})$ and all of its $p$ –primary subgroups are either trivial or not finitely generated as an abelian group. These Nil-groups include the Nil-groups appearing in the decomposition of $K_{i}$ of virtually cyclic groups for $i \leq 1$ .

Keywords

Nil-groups, non-finiteness, twisted Laurent polynomial ring

Mathematical Subject Classification 2000

Primary: 18F25

Secondary: 19B28, 19D35

References

Publication

Received: 6 May 2006

Accepted: 6 September 2006

Published: 18 December 2007

Authors

Joachim Grunewald
Fachbereich Mathematik und Informatik Westfälische Wilhelms-Universität Münster Einsteinstrasse 62 D-48149 Münster Germany

Volume 7, issue 4 (2007)