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New number fields with known $p$-class tower

In: Tatra Mountains Mathematical Publications, vol. 64, no. 3
Daniel Constantine Mayer
Detaily:
Rok, strany: 2015, 21 - 57
Kľúčové slová:
$p$-class field towers, $p$-capitulation, $p$-class groups, quadratic fields, cubic fields, dihedral fields; finite $p$-groups, descendant trees, $p$-group generation algorithm
O článku:
The $p$-class tower $\mathrm{F}p(k)$ of a number field $k$ is its maximal unramified pro-$p$ extension. It is considered to be known when the $p$-tower group, that is the Galois group $G:=\mathrm{Gal}(\mathrm{F}p(k)\vert k)$, can be identified by an explicit presentation. The main intention of this article is to characterize assigned finite $3$-groups uniquely by abelian quotient invariants of subgroups of finite index, and to provide evidence of actual realizations of these groups by $3$-tower groups $G$ of real quadratic fields $K=\mathbb{Q}(\sqrt{d})$ with $3$-capitulation type $(0122)$ or $(2034)$.
Ako citovať:
ISO 690:
Mayer, D. 2015. New number fields with known $p$-class tower. In Tatra Mountains Mathematical Publications, vol. 64, no.3, pp. 21-57. 1210-3195.

APA:
Mayer, D. (2015). New number fields with known $p$-class tower. Tatra Mountains Mathematical Publications, 64(3), 21-57. 1210-3195.