English

New number fields with known p-class tower

Number Theory 2015-10-05 v1

Abstract

The p-class tower Fp(k)F_p^\infty(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:=Gal(Fp(k)/k)G:=Gal(F_p^\infty(k)/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=Q(d)K=Q(\sqrt{d}) with 3-capitulation type (0122) or (2034).

Keywords

Cite

@article{arxiv.1510.00565,
  title  = {New number fields with known p-class tower},
  author = {Daniel C. Mayer},
  journal= {arXiv preprint arXiv:1510.00565},
  year   = {2015}
}

Comments

25 pages, 5 figures; presented at the 22nd Czech and Slovak International Conference on Number Theory in Liptovsky Jan, Slovakia, on August 31, 2015

R2 v1 2026-06-22T11:11:15.791Z