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The natural automorphism group of a translation surface is its group oftranslations. For finite translation surfaces of genus g > 1 the order of thisgroup is naturally bounded in terms of g due to a Riemann-Hurwitz formulaargument. In analogy with classical Hurwitz surfaces, we call surfaces whichachieve the maximal bound Hurwitz translation surfaces. We study for which gthere exist Hurwitz translation surfaces of genus g.

Finite translation surfaces with maximal number of translations