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Abstract. 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 .

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Abstract. Answering a question by Stark, we show that for an infinite unramified pro-p-extension of a number field k, the p-class numbers of its finite subextensions tend to infinity. This is proven by means of a group-theoretical result on compact p-adic analytic groups. Furthermore, we provide an equivalent formulation of the FontaineMazur conjecture for p-extensions unramified outside a finite set of primes not containing any prime above p.