论文标题
基本类型的符号长度 - $ $ p $组和梅西产品
The symbol length for elementary type pro-$p$ groups and Massey products
论文作者
论文摘要
对于Prime Number $ P $和整数$ M \ GEQ2 $，我们证明$ h^2中的所有元素的符号长度（g，\ sathbb {f} _p）$，用于Pro- $ P $ p $ g $ G $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $（m^2/4）+m^2/4）+m $ m $ m $。假设基本类型的猜想，这适用于所有有限生成的最大pro-p $ p $ galois组$ g = g = g_f（p）字段$ f $，其中包含订单$ p $ unity unity的根。更一般地，我们为给定的同胞元素$ \barΩ\barΩ Pro-P $组同态。
For a prime number $p$ and an integer $m\geq2$, we prove that the symbol length of all elements of $m$-fold Massey products in $H^2(G,\mathbb{F}_p)$, for pro-$p$ groups $G$ of elementary type, is bounded by $(m^2/4)+m$. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-$p$ Galois groups $G=G_F(p)$ of fields $F$ which contain a root of unity of order $p$. More generally, we provide such a uniform bound for the symbol length of all pullbacks $ρ^*(\barω)$ of a given cohomology element $\barω\in H^n(\bar G,\mathbb{F}_p)$, where $\bar G$ is a finite $p$-group, $n\geq2$, and $ρ\colon G\to \bar G$ is a pro-$p$ group homomorphism.
