A Class of Groups in Which All Unconditionally Closed Sets are Algebraic
Group Theory
2007-05-23 v2 General Topology
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.
Keywords
Cite
@article{arxiv.math/0610430,
title = {A Class of Groups in Which All Unconditionally Closed Sets are Algebraic},
author = {Ol'ga V. Sipacheva},
journal= {arXiv preprint arXiv:math/0610430},
year = {2007}
}
Comments
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