The word you want is semigroup: http://en.wikipedia.org/wiki/Semigroup Well, there is this: http://en.wikipedia.org/wiki/Light's_associativity_test And you might find something of interest in the reference to this OEIS entry: number of semigroups of order n http://oeis.org/A001423 On Tue, Aug 19, 2014 at 9:02 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I'm interested in binary operations on a finite set S that are associative, period; no other constraints.
1. Are there "fast" methods for checking associativity given the operation table?
2. Can all such associative operations be emulated "efficiently" using an isomorphism in which the operation is matrix multiplication (not just over standard rings, but extended like Knuth & the APL language do) ?
(RCS knows why I'm asking this question.)
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