I am looking for examples of nilpotent connected (or at least almost connected) locally compact groups which are not Lie groups. Do you know of such examples ?
2026-03-26 14:24:45.1774535085
Examples of nilpotent connected locally compact groups which are not Lie groups
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The infinite product ${\mathbb S}^1 \times {\mathbb S}^1 \times ...$ satisfies this requirement. It is abelian, compact and connected, but it is not a Lie group because it has an infinite, strictly increasing chain of connected, closed subgroups.