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Summary
A semigroup is a set with an associative binary operation (which may not contain an identity element). The commuting probability of a semigroup is the probability that two elements chosen at random commute with each other. In this paper, we construct a single family of semigroups which achieves each positive rational in the interval (0, 1] as a commuting probability.
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Notes on contributors
Michelle Soule
Michelle Soule ([email protected]) is from San Diego, California. She graduated with a B.S. in mathematics from California State University, Long Beach, in 2010. She received an M.A. in mathematics from San Diego State University in 2013. She is currently attending the University of Wisconsin at Madison, working toward a Ph.D. in mathematics. In her free time, she enjoys cooking, playing cards, and hiking with her golden retriever.