关于正特征的Noether界和Weyl界
On Noether's and Weyl's bound in positive characteristic
摘要：
本文将有限群的不变量从特征零推广到不整除群阶的正特征。第一个是施密德的相对版本的诺特定理。该定理比较了群的生成元与子群的生成元的度。然后，我们证明了一个合适的积极的特征版本的外尔定理的矢量不变量：极化工程在小程度上。利用这一点，我们证明了正则表示具有“最一般”的不变量环，从而推广了Schmid和Smith的定理。
英文摘要：
In this note we generalize several well known results concerning invariants of finite groups from characteristic zero to positive characteristic not dividing the group order. The first is Schmid's relative version of Noether's theorem. That theorem compares the degrees of generators of a group with those of a subgroup. Then we prove a suitable positive characteristic version of Weyl's theorem on vector invariants: polarization works in small degrees. Using that we show that the regular representation has the "most general" ring of invariants, thereby generalizing theorems of Schmid and Smith.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
