The Probability that Two Semigroup Elements Commute Can Be Almost Anything

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The title indicates the content of this capsule. Among all finite semigroups, the set of probabilities that two elements commute is dense in [0, 1]. (This is in contrast to the fact that the corresponding probability for a non-Abelian group is never greater than ⅝).

Document Type: Miscellaneous

Publication date: November 1, 2008

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