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Commuting probability
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and more precisely in <a href="/facts/Group_theory/NfowcI5H">group theory</a>, the commuting probability (also called degree of commutativity or commutativity degree) of a <a href="/facts/Finite_group/vv2tvogB">finite group</a> is the <a href="/facts/Probability/fgYvMhwb">probability</a> that two randomly chosen elements <a href="/facts/Commutative_property/WaYxJLxd">commute</a>. It can be used to measure how close to <a href="/facts/Abelian_group/FfWwmx4R">abelian</a> a finite group is. It can be generalized to infinite <a href="/facts/Group_(mathematics)/IQTYqINt">groups</a> equipped with a suitable <a href="/facts/Probability_measure/8BjhgoPR">probability measure</a>, and can also be generalized to other <a href="/facts/Algebraic_structure/TkuXca24">algebraic structures</a> such as <a href="/facts/Ring_(mathematics)/JnCUXz63">rings</a>. </p>