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Is there a standard notation for the n-fold free product of a group with itself? In particular, I'd like to know a nice name or notation for the the $n$-fold free product of $\mathbb Z/2\mathbb Z$ with itself.

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    Reverted to asterisks because the OP was not referring to the Cartesian product.2012-08-27

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I have repeatedly seen $G^{*n}$ as a notation for the n-fold free product. It seems clear and unambiguous enough for me.