SOME EXAMPLES OF FAB AND MILD PRO-p-GROUPS WITH TRIVIAL CUP-PRODUCT

Let G(s) be the Galois group of the maximal pro-p-extension Q(s) of Q unramified outside a finite set S of places of Q not containing the prime p > 2. In this work, we develop a method to produce some examples of mild (and thus FAB) pro-p-groups G(s) for which some relations are of degree three (according to the Zassenhaus filtration). The key computation are done in some Heisenberg extensions of Q of degree p(3). With the help of GP-Pari we produce some examples for p = 3.