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Embdfinal

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Mathematics
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University Of California Los Angeles
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1. Let G be a finite group. Let us say (only for this specific question) that the embedding degree of G is the smallest positive integer n such that there exists an injective group homomorphism ϕ : G ,→ Sn from G to the symmetric group Sn . Equivalently, the embedding degree of G is the smallest value of n such that G is isomorphic to a subgroup of Sn . We write embd(G) for the embedding degree of G. (a) Show that the embedding degree is equal to the smallest positive integer n such that there exists a faithful action of G on a set with n elements. . Each action of G on a set of n elements ...
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