R\'edei symbols and arithmetical mild pro-2-groups
Jochen G\"artner

TL;DR
This paper describes the triple Massey product for certain Galois groups using Rédéi symbols, showing the existence of specific mild pro-2-groups with particular properties.
Contribution
It provides an explicit description of the triple Massey product for Galois groups and constructs examples of mild pro-2-groups with Zassenhaus invariant 3.
Findings
Explicit description of triple Massey product via Rédéi symbols
Existence of mild pro-2-groups with Zassenhaus invariant 3 as Galois groups
Construction of a non-analytic mild fab pro-2-group with 3 generators
Abstract
Generalizing results of Morishita and Vogel, an explicit description of the triple Massey product for the Galois group of the maximal 2-extension of unramified outside a finite set of prime numbers containing 2 is given in terms of R\'edei symbols. We show that mild pro-2-groups with Zassenhaus invariant 3 occur as Galois groups of the form . Furthermore, a non-analytic mild fab pro-2-group having only 3 generators is constructed .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
