论文标题
Galois Wheoretic功能1平滑的Pro- $ P $组
Galois-theoretic features for 1-smooth pro-$p$ groups
论文作者
论文摘要
令$ p $为素数。如果可以将其赋予连续表示$θ\ colon g \ to \ mathrm {gl} _1（\ Mathbb {z} _p）$，则可以将其连续表示$θ\ colon g \ to pro-p $ $ g $，据说是1平滑的每个1平滑的Pro-P $组都包含一个独特的最大封闭的Abelian普通亚组，与Engler和Koenigsmann的结果相比，在最大范围内的田野群体上，如果可以解决1平方英尺的Proi-P $组，那么它是可解决的，然后是本地均匀的组合，与MAXIM相比，它是在MAXIM上的批准，而Pros y Max $ pros cal of pros of pros of pros of pros of pros of pros of ware pros of ware of ware of ware of ware of ware of ware of ware。最后，我们询问1平滑的Pro-P $组是否满足“山雀”的替代方案。
Let $p$ be a prime. A pro-$p$ group $G$ is said to be 1-smooth if it can be endowed with a continuous representation $θ\colon G\to\mathrm{GL}_1(\mathbb{Z}_p)$ such that every open subgroup $H$ of $G$, together with the restriction $θ\vert_H$, satisfies a formal version of Hilbert 90. We prove that every 1-smooth pro-$p$ group contains a unique maximal closed abelian normal subgroup, in analogy with a result by Engler and Koenigsmann on maximal pro-$p$ Galois groups of fields, and that if a 1-smooth pro-$p$ group is solvable, then it is locally uniformly powerful, in analogy with a result by Ware on maximal pro-$p$ Galois groups of fields. Finally we ask whether 1-smooth pro-$p$ groups satisfy a "Tits' alternative".
