Denote by $G_0$ the identity connected component of a topological group $G$. Is there a compact group $G$ such that
- $G_0$ is abelian group,
- $Z(G)$ does not contain $G_0$, and
- $G_0$ is of (Haar) measure zero in $G$?
2026-03-27 12:30:17.1774614617
An example of a compact group which its identity connected component is nontrivial, abelian and of measure zero.
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