We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸ⁿ is as large as possible, namely, equal to the normal closure of the special linear group in the special automorphism group. In particular, we investigate m-triangular automorphisms, i.e., those that can be expressed as a product of affine automorphisms and m triangular automorphisms. Over a field of characteristic zero, we show that every nontrivial 4-triangular special automorphism generates the entire normal closure of the special linear group in the special tame subgroup, for any dimension n ≥ 2. This generalizes a result of Furter and Lamy in dimension 2.

中文翻译：

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由单多项式自态生成的正常子群

我们研究确定由单个特殊多项式自同构morph ⁿ生成的正规子群何时尽可能大的准则，即等于特殊特殊同构群中特殊线性群的正规闭合。特别是，我们研究了m三角自同构，即那些可以表示为仿射自同构和m三角自同构的乘积。在特征为零的字段上，我们表明对于任何维度n≥2，每个非平凡的4三角形特殊自同构都会生成特殊驯服亚组中特殊线性组的整个法线闭合。这概括了Furter和Lamy在尺寸上的结果2。