---
tag: MJC27Y35HH
kind: concept
name: Light's associativity test
aliases: [associativity-test, lights-test-for-associativity]
sources:
  - wikipedia: en:22783408@r1318996839
    locator: Light's associativity test
    note: adopted
    mention: wikipedia://en/22783408
    sections: [Summary]
same_as:
  wikidata: Q6545927
  wikipedia: Light's associativity test
inventory: [JX5HHVT39V]
---

## Summary

In 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 $n$).