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  "aliases": [
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  "body": "\n## Summary\n\nIn mathematics, **Light's associativity test** is a procedure invented by F. W. Light for testing whether a [[binary operation|0580ZJSA3Q]] defined in a [[finite set|070R982G4B]] by a [[Cayley multiplication table|0E4WH0R7HG]] is associative. The naive procedure for verification of the associativity of a binary operation specified by a Cayley table, which compares the two products that can be formed from each triple of elements, is cumbersome. Light's associativity test simplifies the task in some instances (although it does not improve the worst-case runtime of the naive algorithm, namely $\\mathcal{O} \\left( n^{3} \\right)$ for sets of size $n$).\n",
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