Let $G$ be a compact connected Lie group. Then there exist an integer $k\geq 0$, a simply connected compact semisimple Lie group $K$, and a finite subgroup
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\begin{align*}
F\leq T^k\times Z(K)
\end{align*}
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such that $F$ is central in $T^k\times K$ and there is an isomorphism of Lie groups