Relations in the maximal pro-𝑝 quotients of absolute Galois groups

Abstract

We observe that some fundamental constructions in Galois theory can be used to obtain interesting restrictions on the structure of Galois groups of maximal p p -extensions of fields containing a primitive p p -th root of unity. This is an extension of some significant ideas of Demushkin, Labute, and Serre from local fields to all fields containing a primitive p p -th root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.