Geodesic
Non-finiteness results for Nil-groups
Grunewald, Joachim1
1Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität Münster, Einsteinstrasse 62, D-48149 Münster, Germany
Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1979-1986
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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.

DOI : 10.2140/agt.2007.7.1979
Keywords: Nil-groups, non-finiteness, twisted Laurent polynomial ring

Grunewald, Joachim  1

1 Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität Münster, Einsteinstrasse 62, D-48149 Münster, Germany 
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Grunewald, Joachim. Non-finiteness results for Nil-groups. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1979-1986. doi: 10.2140/agt.2007.7.1979

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