Abstract
Let be the field of complex numbers and n and k natural numbers satisfying and Let be the subset of nth symmetric product of with itself consisting of n-point sets in general position and let We describe the dimension of the points in which correspond to n-point sets whose automorphism group contains a subgroup of prime order. From this result, we prove that the points in which correspond to n-point sets with nontrivial automorphism group form a proper subset
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