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* For all and the commutator is in
* Any two elements commute modulo the normal subgroup membership relation. That is, for all if and only if

Examples

For any group the trivial subgroup consisting of just the identity element of is always a normal subgroup of Likewise, itself is always a normal subgroup of (If these are the only normal subgroups, then is said to be simple.) Other named normal subgroups of an arbitrary group

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