I seem to recall that there is a relatively easy method for determining the associativity of an operation by using its Cayley table. What is it?
It is called Light's associativity test which I found on Wikipedia.
- Pick out the generators of the operation.
- If $g$ is a generator define two new operations $x \circ y = (xg)y $ and $x*y=x(gy)$.
- Form the Cayley tables of $\circ$ and $*$ for $g$.
- If the two tables for $g$ are not identical, the original operation is NOT associative.
- If the two tables are identical for all generators $g$, the original operation IS associative.
Notwithstanding the first comment, the link above works now, Nov 7, thanks to a kind editor.