I would like to find an example of locally compact connected group $G$ which the commutator subgroup $G$ is not $G$ itself.
2026-03-25 19:03:42.1774465422
An example of locally compact connected group which is not perfect
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What about $\mathrm{GL}(n,\mathbb R)_+$ (that is $\{g\in\mathrm{GL}(n,\mathbb R)\mid\det g>0\}$)? Its commutator subgroup is $\mathrm{SL}(n,\mathbb R)$.