We provide a simple criterion for an element of the mapping class group of a closed surface to be a normal generator for the mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator for the mapping class group when the genus is at least 3. We also give many examples of pseudo-Anosov normal generators, answering a question of D. D. Long. In fact we show that every pseudo-Anosov mapping class with stretch factor less than $\sqrt{2}$ is a normal generator. Even more, we give pseudo-Anosov normal generators with arbitrarily large stretch factors and arbitrarily large translation lengths on the curve graph, disproving a conjecture of Ivanov.

中文翻译：

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映射类组的法线生成器很丰富

我们为封闭曲面的映射类组的元素提供了一个简单的标准，使其成为映射类组的法线生成器。我们应用它来证明当属至少为 3 时，每个非超椭圆对合的非平凡周期映射类都是映射类群的法线生成器。我们还给出了许多伪阿诺索夫法线生成器的示例，回答了以下问题DD龙。事实上，我们证明每个拉伸因子小于 $\sqrt{2}$ 的伪 Anosov 映射类都是正常的生成器。更重要的是，我们在曲线图上给出了具有任意大拉伸因子和任意大平移长度的伪阿诺索夫法线生成器，反驳了伊万诺夫的猜想。