The probability that two uniform random elements of a finite group commute with each other
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.[1][2] 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,[3] and can also be generalized to other algebraic structures such as rings.[4]
^Gustafson, W. H. (1973). "What is the Probability that Two Group Elements Commute?". The American Mathematical Monthly. 80 (9): 1031–1034. doi:10.1080/00029890.1973.11993437.
^Das, A. K.; Nath, R. K.; Pournaki, M. R. (2013). "A survey on the estimation of commutativity in finite groups". Southeast Asian Bulletin of Mathematics. 37 (2): 161–180.
^Cite error: The named reference :0 was invoked but never defined (see the help page).
^Cite error: The named reference :1 was invoked but never defined (see the help page).
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