A note on free pro-p-extensions of algebraic number fields
Journal de théorie des nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 165-178.

For an algebraic number field k and a prime p, define the number ρ to be the maximal number d such that there exists a Galois extension of k whose Galois group is a free pro-p-group of rank d. The Leopoldt conjecture implies 1≤ρ≤r 2 +1, (r 2 denotes the number of complex places of k). Some examples of k and p with ρ=r 2 +1 have been known so far. In this note, the invariant ρ is studied, and among other things some examples with ρ<r 2 +1 are given.

Mots-clés : algebraic number field, $\mathbb {Z}_p$-extension, free pro-$p$-group 
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Yamagishi, Masakazu. A note on free pro-$p$-extensions of algebraic number fields. Journal de théorie des nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 165-178. http://archive.numdam.org/item/JTNB_1993__5_1_165_0/

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