Mild pro-\(p\)-groups as Galois groups over global fields. (English) Zbl 1232.11121
In [J. Reine Angew. Math. 596, 155–182 (2006; Zbl 1122.11076)], J. Labute introduced a class of pro-\(p\)-groups, called mild groups, showing some interesting properties in the case of odd \(p\). He also proves that such groups occur as Galois groups of the maximal \(S\)-ramified pro-\(p\)-extension of \(\mathbb Q\), for certain prime numbers \(p\) and sets of primes \(S\).
In the paper under review, the author finds some new examples of mild groups which are Galois groups of global fields. In particular the kind of field extensions which are considered are maximal \(T\)-split \(S\)-ramified pro-\(p\)-extensions, both of function fields and number fields.
In the paper under review, the author finds some new examples of mild groups which are Galois groups of global fields. In particular the kind of field extensions which are considered are maximal \(T\)-split \(S\)-ramified pro-\(p\)-extensions, both of function fields and number fields.
Reviewer: Alessandro Cobbe (Cervignano del Friuli)
MSC:
| 11R37 | Class field theory |
| 11R32 | Galois theory |
| 11R58 | Arithmetic theory of algebraic function fields |
| 11R21 | Other number fields |
Citations:
Zbl 1122.11076References:
| [1] | DOI: 10.1016/j.jalgebra.2006.08.002 · Zbl 1119.20033 · doi:10.1016/j.jalgebra.2006.08.002 |
| [2] | DOI: 10.1007/978-3-662-11323-3 · doi:10.1007/978-3-662-11323-3 |
| [3] | DOI: 10.5802/jtnb.233 · Zbl 0938.11052 · doi:10.5802/jtnb.233 |
| [4] | DOI: 10.1006/jnth.1997.2158 · Zbl 0896.11043 · doi:10.1006/jnth.1997.2158 |
| [5] | DOI: 10.1007/978-3-662-04967-9 · doi:10.1007/978-3-662-04967-9 |
| [6] | Labute J., J. Reine Angew. Math. 596 pp 155– |
| [7] | Neukirch J., Grundlehren der Mathematischen Wissenschaften, in: Cohomology of Number Fields (2000) |
| [8] | Schmidt A., J. Reine Angew. Math. 596 pp 115– |
| [9] | Schmidt A., Doc. Math. |
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