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arXiv · 1303.2608

R\'edei symbols and arithmetical mild pro-2-groups

Jochen Gärtner
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Abstract

Generalizing results of Morishita and Vogel, an explicit description of the triple Massey product for the Galois group $G_S(2)$ of the maximal 2-extension of $\mathbb{Q}$ unramified outside a finite set of prime numbers $S$ 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 $G_S(2)$. Furthermore, a non-analytic mild fab pro-2-group having only 3 generators is constructed .

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Jochen Gärtner. 2013-03-11. R\'edei symbols and arithmetical mild pro-2-groups. https://arxiv.org/abs/1303.2608

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