Meaning of closed under an associative product

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I know the meaning of associative binary operation. I know the meaning of closed under a binary operation. Does closed under an associative product means:

$$ a*(b*c) \in G \implies (a*b)*c \in G$$

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2 Answers

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No. It means closed under a product, which happens to be associative.

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(closd under associative product *) = (closed under product *) + (product * is associative).

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