On the descending central sequence of absolute Galois groups
65 citations recorded by the source corpus.
Let $p$ be an odd prime number and $F$ a field containing a primitive $p$th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group $G_F$ of $F$. Namely, the third subgroup $G_F^{(3)}$ in the descending $p$-central sequence of $G_F$ is the intersection of all open normal subgroups $N$ such that $G_F/N$ is $1$, ${\Bbb Z}/p^2$, or the extra-special group $M_{p^3}$ of order $p^3$ and exponent $p^2$.
View Paper: https://www.semanticscholar.org/paper/301f7f64980ba6df335ae72f750827f654f48721
Citations in the corpus
- Triple Massey products and Galois theory (2013, background): “the Kernel n-Unipotent Conjecture (see Conjecture 8.3). As will be explained in Section 8, the Kernel n-Unipotent Conjecture evolved over a number of years through work contained in [Vi],[MS2],[GLMS],[EM1],[EM2] and [Ef2]. This conjecture has significant value because it describes specific pro-p-group”
- The Zassenhaus filtration, Massey Products, and Representations of Profinite Groups (2013, background): “ions ofTheorem A’aresatisfied whenGhasp-cohomological dimension ≤1 (Corollary 11.4). Hence Theorem A is a special case of Theorem A’. Theorem A’ is elementary for n= 1. For n= 2, p= 2 it was proved in [EM11a], generalizing a result of Minaˇc and Spira [MSp96] (see also [NQD12]). For n= 2, p>2 it w”