The R_∞ property for abelian groups

2014/02/08 by Karel Dekimpe, Dekimpe, Karel, Daciberg Lima Gonçalves +2
Mathematics · #20E36 #20K21 #55M20 #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras #math.GR #msc:20E36 #msc:20K21 #msc:55M20

paper · pdf · doi:10.48550/arxiv.1402.1861

8 pages, no figures

arxiv created 2014/02/08 · openalex publication_date 2014/02/08 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known there is no finitely generated abelian group which has the R_∞ property. We will show that also many non-finitely generated abelian groups do not have the R_∞ 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_∞ property. We also construct an abelian group such that the cardinality of the Reidemeister classes is uncountable for any automorphism of that group. 8 pages, no figures

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