I am aware of Light's associativity test for Cayley tables, but I am wondering, is there a clever way to deduce associativity from the set's properties / presentation that permits one to not have compute every single product?
I had a problem that involved deducing whether or not a set is associative given its Cayley table, and, upon confirming with my professor that one indeed has to compute every single product (64 of them!?), he mentioned that such a problem can be greatly simplified by observing certain patterns that seem to emerge in the table (i.e. the set's properties). Can someone give me an example of such a case where this happens?
Thanks in advance.