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Normal subgroups of compact groups

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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. This relies on asymptotic results on the fixed points of automorphisms of finite simple groups and Lie groups. We also prove that the abstract commutator subgroup [H,G] is closed for every closed normal subgroup H of G.

Joint work with Dan Segal, Oxford.

This talk is part of the Algebra seminar series.

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