Let $G$ be a compact Lie group. Then by Levi-Malciv $G=S\cdot Z$ where $Z$ is the connected component of the center and $S$ is the maximal semisimple subgroup.
How to show that $S$ is connected, closed and compact subgroup of $G$?
Let $G$ be a compact Lie group. Then by Levi-Malciv $G=S\cdot Z$ where $Z$ is the connected component of the center and $S$ is the maximal semisimple subgroup.
How to show that $S$ is connected, closed and compact subgroup of $G$?
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