In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g−1). A group for which the maximum is achieved is called a Hurwitz group, and the corresponding Riemann surface a Hurwitz surface. Because compact Riemann surfaces are synonymous with non-singular complex projective algebraic curves, a Hurwitz surface can also be called a Hurwitz curve. The theorem is named after Adolf Hurwitz, who proved it in (Hurwitz 1893).
Read more about Hurwitz's Automorphisms Theorem: Interpretation in Terms of Hyperbolicity, The Idea of A Proof and Construction of The Hurwitz Surfaces, Examples of Hurwitz's Groups and Surfaces
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“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (19131960)