Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 4 (2007), 1979-1986.
Non-finiteness results for Nil-groups
Generalizing an idea of Farrell we prove that for a ring and a ring automorphism of finite order the groups and all of its –primary subgroups are either trivial or not finitely generated as an abelian group. We also prove that if and are ring automorphisms such that is of finite order then and all of its –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 of virtually cyclic groups for .
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 1979-1986.
Received: 6 May 2006
Accepted: 6 September 2006
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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