Volume 7, issue 4 (2007)

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Non-finiteness results for Nil-groups

Joachim Grunewald

Algebraic & Geometric Topology 7 (2007) 1979–1986
Abstract

Generalizing an idea of Farrell we prove that for a ring Λ and a ring automorphism α of finite order the groups Nil0(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 γ is of finite order then Nil0(Λ;Λβ,Λγ) 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 Ki of virtually cyclic groups for i 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