收缩理性与Noether问题

摘要：

设K是任意域，G是有限群.本文证明了：若K是任意域，p是奇素数，G是指数为p的非阿贝尔群，且|G| =p^3或p^4满足[K（n_p）：K] ≤ 2，则K（G）是K上的有理数.我们还将证明K（G）是收缩有理的，如果G属于一个更大的p-群类。特别是，一般的G-多项式的G-Galois扩展存在这些群体。

英文摘要：

Let K be any field and G be a finite group. We will prove that, if K is any field, p an odd prime number, and G is a non-abelian group of exponent p with |G|=p^3 or p^4 satisfying [K(ζ_p):K] <= 2, then K(G) is rational over K. We will also show that K(G) is retract rational if G belongs to a much larger class of p-groups. In particular, generic G-polynomials of G-Galois extensions exist for these groups.

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。