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A complete solution of Markov's problem on connected group topologies
Dikranjan, Dikran N., 1950- ; Shakhmatov, Dmitri
Every proper closed subgroup of a connected Hausdorff group must have index at least ▫$\mathfrak{c}$▫, 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 ▫$\mathfrak{c}$▫. 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.
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