## Topological Methods in Nonlinear Analysis

### The $R_\infty$ property for abelian groups

#### Abstract

It is well known there is no finitely generated abelian group which has the $R_\infty$ property. We will show that also many non-finitely generated abelian groups do not have the $R_\infty$ property, but this does not hold for all of them! In fact we construct an uncountable number of infinite countable abelian groups which do have the $R_{\infty}$ property. We also construct an abelian group such that the cardinality of the Reidemeister classes is uncountable for any automorphism of that group.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 2 (2015), 773-784.

Dates
First available in Project Euclid: 21 March 2016

https://projecteuclid.org/euclid.tmna/1458588661

Digital Object Identifier
doi:10.12775/TMNA.2015.066

Mathematical Reviews number (MathSciNet)
MR3494970

Zentralblatt MATH identifier
1372.20051

#### Citation

Dekimpe, Karel; Gonçalves, Daciberg Lima. The $R_\infty$ property for abelian groups. Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 773--784. doi:10.12775/TMNA.2015.066. https://projecteuclid.org/euclid.tmna/1458588661

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