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The standard symmetry group for a link is the mapping class group $\\MCG(S^3,L)$ or $\\Sym(L)$ of the pair $(S^3,L)$. Elements in this symmetry group can (and often do) fix the link and act nontrivially only on its complement. We ignore such elements and focus on the \"intrinsic\" symmetry group of a link, defined to be the image $\\Sigma(L)$ of the natural homomorphism $\\MCG(S^3,L) \\rightarrow \\MCG(S^3) \\cross \\MCG(L)$. 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