Simple Lie group
ANALOGY: This is an analogue in Lie group of a property encountered in group. Specifically, it is a Lie group property analogous to the group property: simple group
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A Lie group is said to be simple if it does not contain any proper nontrivial connected normal subgroup. (sometimes the definition also requires the Lie group to be connected. Since the connected component is either the whole group or the trivial subgroup, this is not a great loss).