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About: Commuting probability     Goto   Sponge   NotDistinct   Permalink

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In mathematics and more precisely in group theory, the commuting probability (also called degree of commutativity or commutativity degree) of a finite group is the probability that two randomly chosen elements commute. It can be used to measure how close to abelian a finite group is. It can be generalized to infinite groups equipped with a suitable probability measure, and can also be generalized to other algebraic structures such as rings.