Post #1816224
2026-02-22 17:48 UTC
@dwarn Conjecture. Associativity is not needed to reach the same conclusion.
Replies (1)
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@oantolin@mathstodon.xyz 2026-02-22 18:24
@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.