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 1ρr 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.

DOI : https://doi.org/10.5802/jtnb.86
Mots clés : algebraic number field, p -extension, free pro-p-group
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     author = {Yamagishi, Masakazu},
     title = {A note on free pro-$p$-extensions of algebraic number fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {165--178},
     publisher = {Universit\'e Bordeaux I},
     volume = {5},
     number = {1},
     year = {1993},
     doi = {10.5802/jtnb.86},
     zbl = {0784.11052},
     mrnumber = {1251235},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.86/}
}
Masakazu Yamagishi. 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. doi : 10.5802/jtnb.86. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.86/

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