The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering in the mapping class group of the total surface. We prove that the balanced superelliptic mapping class groups with either one marked point, one boundary component, or no marked points and boundary are generated by three elements. To prove this, we also show that its liftable mapping class groups are also generated by three elements. These generating sets are minimal except for several cases of closed surfaces.

中文翻译：

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平衡超椭圆映射类组由三个元素生成

平衡超椭圆映射类群是平衡超椭圆覆盖变换群在总曲面映射类群中的归一化器。我们证明了具有一个标记点​​、一个边界分量或没有标记点和边界的平衡超椭圆映射类组是由三个元素生成的。为了证明这一点，我们还表明它的可提升映射类组也是由三个元素生成的。除了几种封闭曲面的情况外，这些生成组都是最小的。