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2016 Revisiting Farrell's nonfiniteness of Nil
Jean-François Lafont, Stratos Prassidis, Kun Wang
Ann. K-Theory 1(2): 209-225 (2016). DOI: 10.2140/akt.2016.1.209


We study Farrell Nil-groups associated to a finite-order automorphism of a ring R. We show that any such Farrell Nil-group is either trivial or infinitely generated (as an abelian group). Building on this first result, we then show that any finite group that occurs in such a Farrell Nil-group occurs with infinite multiplicity. If the original finite group is a direct summand, then the countably infinite sum of the finite subgroup also appears as a direct summand. We use this to deduce a structure theorem for countable Farrell Nil-groups with finite exponent. Finally, as an application, we show that if V is any virtually cyclic group, then the associated Farrell or Waldhausen Nil-groups can always be expressed as a countably infinite sum of copies of a finite group, provided they have finite exponent (which is always the case in dimension zero).


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Jean-François Lafont. Stratos Prassidis. Kun Wang. "Revisiting Farrell's nonfiniteness of Nil." Ann. K-Theory 1 (2) 209 - 225, 2016.


Received: 23 February 2015; Accepted: 31 March 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1330.18019
MathSciNet: MR3514940
Digital Object Identifier: 10.2140/akt.2016.1.209

Primary: 18E10, 18F25, 19D35

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.1 • No. 2 • 2016
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