Rédei symbols and arithmetical mild pro-2-groups

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Generalizing results of Morishita and Vogel, an explicit description of the triple Massey product for the Galois group Gₛ(2) of the maximal 2-extension of Q unramified outside a finite set of prime numbers S containing 2 is given in terms of Rédei symbols. We show that mild pro-2-groups with Zassenhaus invariant 3 occur as Galois groups of the form Gₛ(2). Furthermore, a non-analytic mild fab pro-2-group having only 3 generators is constructed.