Displaying similar documents to “A note on free pro-p-extensions of algebraic number fields.”

A note on free pro- p -extensions of algebraic number fields

Masakazu Yamagishi (1993)

Journal de théorie des nombres de Bordeaux


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.