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

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

2006-10-13

arxiv.org/abs/math/0610430v2

Mathematics

Group Theory

Version 2: A mistake noticed by D. Dikranjan and D. Shakhmatov is corrected. The main theorem is valid only for subgroups $H$

Scientific paper

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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