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