Algebraic & Geometric Topology

Non-finiteness results for Nil-groups

Joachim Grunewald

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
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

Subjects
Primary: 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
Secondary: 19B28: $K_1$of group rings and orders [See also 57Q10] 19D35: Negative $K$-theory, NK and Nil

Keywords
Nil-groups non-finiteness twisted Laurent polynomial ring

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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