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abelian group abelian subgroup algebraic arcs arithmetic mean boundary circle class ft coefficients collineation columns conics conjugate constant converges uniformly corresponding curve cusp cycle cyclic cyclic group denote discriminant edges equal essential singularities essentially linearly dependent expression factor finite number follows formula Gaussian law given group of order H. A. Schwarz Hence infinite integral intersection interval invariant plane invariant three-chain involutoric Laplace's equation linearly dependent locus matrix metacyclic group monodromie group n-cells necessary and sufficient non-abelian group non-invariant norm obtained order pm orthogonal pair parameters parametric equations pencil positive probability problem proof proved quadratic quadratic transformation Quartic Equations rational rational curves relation remain finite represented roots satisfy solution square subgroup of index substitution sufficient condition Sylow subgroup tangent theorem three binary quintics three-chain contains Type vanish variables vertex vertices write