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Commutator
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<p> In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the commutator gives an indication of the extent to which a certain <a href="/facts/Binary_operation/CYtow0bz">binary operation</a> fails to be <a href="/facts/Commutative/WaYxJLxd">commutative</a>. There are different definitions used in <a href="/facts/Group_theory/NfowcI5H">group theory</a> and <a href="/facts/Ring_theory/VW6svEFe">ring theory</a>. </p>