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Abstract : 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-$p$-group $\G S$ for which some relations are of degree~$3$ 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 $p=3$.





Autor: Christian Maire -

Fuente: https://hal.archives-ouvertes.fr/



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