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2007 Non-finiteness results for Nil-groups
Joachim Grunewald
Algebr. Geom. Topol. 7(4): 1979-1986 (2007). 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 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 βγ 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 i1.

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Joachim Grunewald. "Non-finiteness results for Nil-groups." Algebr. Geom. Topol. 7 (4) 1979 - 1986, 2007. https://doi.org/10.2140/agt.2007.7.1979

Information

Received: 6 May 2006; Accepted: 6 September 2006; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1127.19004
MathSciNet: MR2366184
Digital Object Identifier: 10.2140/agt.2007.7.1979

Subjects:
Primary: 18F25
Secondary: 19B28, 19D35

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.7 • No. 4 • 2007
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