论文标题
Pro-P $组的更高维代数光纤
Higher dimensional algebraic fiberings for pro-$p$ groups
论文作者
论文摘要
我们证明了较高维度代数纤维的某些条件 - $ $ p $组扩展，我们建立了有关pro-$ p $组不连贯性的推论。 In particular, if $G = K \rtimes Γ$ is a pro-$p$ group, $Γ$ a finitely generated free pro-$p$ group with $d(Γ) \geq 2$, $K$ a finitely presented pro-$p$ group with $N$ a normal pro-$p$ subgroup of $K$ such that $K/ N \simeq \mathbb{Z}_p$ and $N$ not有限地生成了一个亲$ P $组，然后$ g $是不一致的（在Pro-P $组类别中）。此外，我们表明，如果$ k $是一个免费的pro-p $组，$ d（k）= 2 $，那么$ aut_0（k）$是不连贯的（在pro-$ p $ groups的类别中），或者有限地呈现pro-p $ grout，而没有procyc $ p $ p $ up-subips proupp $ proups proups proups fin i.ee nocient i.ee nocient，则是clocycllic procyc $ p $ p $。 Bieri-Strebel的结果的Pro-P $版本不持有。
We prove some conditions for higher dimensional algebraic fibering of pro-$p$ group extensions and we establish corollaries about incoherence of pro-$p$ groups. In particular, if $G = K \rtimes Γ$ is a pro-$p$ group, $Γ$ a finitely generated free pro-$p$ group with $d(Γ) \geq 2$, $K$ a finitely presented pro-$p$ group with $N$ a normal pro-$p$ subgroup of $K$ such that $K/ N \simeq \mathbb{Z}_p$ and $N$ not finitely generated as a pro-$p$ group, then $G$ is incoherent (in the category of pro-$p$ groups). Furthermore we show that if $K$ is a free pro-$p$ group with $d(K) = 2$ then either $Aut_0(K)$ is incoherent (in the category of pro-$p$ groups) or there is a finitely presented pro-$p$ group, without non-procyclic free pro-$p$ subgroups, that has a metabelian pro-$p$ quotient that is not finitely presented i.e. a pro-$p$ version of a result of Bieri-Strebel does not hold.
