A complete solution of Markov's problem on connected group topologies
General Topology
2015-10-07 v1 Group Theory
Abstract
Every proper closed subgroup of a connected Hausdorff group must have index at least c, the cardinality of the continuum. 70 years ago Markov conjectured that a group G can be equipped with a connected Hausdorff group topology provided that every subgroup of G which is closed in all Hausdorff group topologies on G has index at least c. Counter-examples in the non-abelian case were provided 25 years ago by Pestov and Remus, yet the problem whether Markov's Conjecture holds for abelian groups G remained open. We resolve this problem in the positive.
Keywords
Cite
@article{arxiv.1509.06660,
title = {A complete solution of Markov's problem on connected group topologies},
author = {Dikran Dikranjan and Dmitri Shakhmatov},
journal= {arXiv preprint arXiv:1509.06660},
year = {2015}
}