View source for Lie group, derived

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The [[Commutator subgroup|commutator subgroup]] of a [[Lie group|Lie group]]. For any Lie group $G$ its derived Lie group $[G,G]$ is a normal (not necessarily closed) Lie subgroup of $G$. The corresponding ideal of the [[Lie algebra|Lie algebra]] $\mathfrak g$ of the group $G$ coincides with the commutator algebra $[\mathfrak g,\mathfrak g]$ (also called the derived Lie algebra of $\mathfrak g$). The commutator subgroup of a simply-connected (or connected linear) Lie group $G$ is always closed in $G$.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  C. Chevalley,   "Theory of Lie groups" , '''1''' , Princeton Univ. Press  (1946)</TD></TR></table>