Nikolay Nikolov, Dan Segal
Abstract
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Among compact Hausdorff groups G whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup [H,G] is closed for every closed normal subgroup H of G.
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Among compact Hausdorff groups G whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup [H,G] is closed for every closed normal subgroup H of G.
Key concepts: Normal subgroup, Commutator subgroup, Mathematics, Quotient, Profinite group, Index of a subgroup, Hausdorff space, Characteristic subgroup