For an algebraic number field and a prime , define the number to be the maximal number such that there exists a Galois extension of whose Galois group is a free pro--group of rank . The Leopoldt conjecture implies , ( denotes the number of complex places of ). Some examples of and with have been known so far. In this note, the invariant is studied, and among other things some examples with are given.
@article{JTNB_1993__5_1_165_0, 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}, mrnumber = {1251235}, zbl = {0784.11052}, language = {en}, url = {http://archive.numdam.org/item/JTNB_1993__5_1_165_0/} }
TY - JOUR AU - Yamagishi, Masakazu TI - A note on free pro-$p$-extensions of algebraic number fields JO - Journal de théorie des nombres de Bordeaux PY - 1993 SP - 165 EP - 178 VL - 5 IS - 1 PB - Université Bordeaux I UR - http://archive.numdam.org/item/JTNB_1993__5_1_165_0/ LA - en ID - JTNB_1993__5_1_165_0 ER -
Yamagishi, Masakazu. A note on free pro-$p$-extensions of algebraic number fields. Journal de théorie des nombres de Bordeaux, Volume 5 (1993) no. 1, pp. 165-178. http://archive.numdam.org/item/JTNB_1993__5_1_165_0/
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