Massey products in the Galois cohomology of number fields

Abstract

We study the relation structure of the Galois group of the maximal outside a finite set of primes unramified p-extension of Q and of the Galois group of the p-class field tower of a quadratic number field. This relation structure is described in terms of Massey products in the Galois cohomology of number fields. A connection is given to Milnor invariants and Redei symbols. In particluar, we prove a number theoretic analogue of the theorem of Porter and Turaev from link theory.