## Algebraic & Geometric Topology

### Non-finiteness results for Nil-groups

Joachim Grunewald

#### 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 $i≤1$.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 1979-1986.

Dates
Accepted: 6 September 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796779

Digital Object Identifier
doi:10.2140/agt.2007.7.1979

Mathematical Reviews number (MathSciNet)
MR2366184

Zentralblatt MATH identifier
1127.19004

#### Citation

Grunewald, Joachim. Non-finiteness results for Nil-groups. Algebr. Geom. Topol. 7 (2007), no. 4, 1979--1986. doi:10.2140/agt.2007.7.1979. https://projecteuclid.org/euclid.agt/1513796779

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