English

p-Tower Groups over Quadratic Imaginary Number Fields

Number Theory 2010-08-19 v1 Group Theory

Abstract

The modern theory of class field towers has its origins in the study of the p-class field tower over a quadratic imaginary number field, so it is fitting that this problem be the first in the discipline to be nearing a solution. We survey the state of the subject and present a new cohomological condition for a quadratic imaginary number field to have an infinite p-class field tower (for p odd). Under an additional hypothesis, we refine this to a necessary and sufficient condition and describe an algorithm for evaluating this condition for a given quadratic imaginary number field.

Keywords

Cite

@article{arxiv.1008.3003,
  title  = {p-Tower Groups over Quadratic Imaginary Number Fields},
  author = {Cam McLeman},
  journal= {arXiv preprint arXiv:1008.3003},
  year   = {2010}
}

Comments

10 pages

R2 v1 2026-06-21T16:02:10.551Z