Post #1816225

@MartinEscardo @dwarn Counterexample: BZ/3 with the operations induced by the group homomorphism Z/3 x Z/3 --> Z/3 given by (x,y) |--> -x-y. That is clearly commutative and it is idempotent because -2 = 1. It is easy to see the homomorphism is not associative, so the map it induces on BZ/3 is not associative on pi_1 either.