A Class of Groups in Which All Unconditionally Closed Sets are Algebraic

2006/10/13 by Ol’ga Sipacheva, Ol'ga V. Sipacheva, Sipacheva, Ol'ga V.
Mathematics · #22A05 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras #Secondary 54H11 #math.GN #math.GR #msc:22A05 #msc:54H11

paper · pdf · doi:10.48550/arxiv.math/0610430

Version 2: A mistake noticed by D. Dikranjan and D. Shakhmatov is corrected. The main theorem is valid only for subgroups $H$ of a direct product of countable groups whose intersections with any countable subproducts are supernormal in $H$. In the proof, two words are changed ("normal" replaced by "supernormal"). Two corollaries are added

openalex publication_date 2006/10/13 · arxiv created 2007/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian groups.

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