Compact extensions of compactly generated nilpotent groups are pro-Lie

Hofmann, Karl H.; Liukkonen, John R.; Mislove, Michael W.

doi:10.1090/S0002-9939-1982-0640250-1

Compact extensions of compactly generated nilpotent groups are pro-Lie
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by Karl H. Hofmann, John R. Liukkonen and Michael W. Mislove

Proc. Amer. Math. Soc. 84 (1982), 443-448

DOI: https://doi.org/10.1090/S0002-9939-1982-0640250-1

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Abstract:

We show that compact extensions of compactly generated (locally compact) pro-Lie groups are pro-Lie, and that compactly generated (locally compact) nilpotent groups are pro-Lie. As a consequence compact extensions of compactly generated nilpotents are pro-Lie. We give examples indicating limitations to extending our results.

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