Periodic sequences of p-class tower groups
Abstract
Recent examples of periodic bifurcations in descendant trees of finite p-groups with p in {2,3} are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p-class group of type (2,2,2), resp. (3,3), form periodic sequences in the descendant tree of the elementary abelian root C(2)xC(2)xC(2), resp. C(3)xC(3). The particular vertex of the periodic sequence which occurs as the p-class tower group G of an assigned field K is determined uniquely by the p-class number of a quadratic, resp. cubic, auxiliary field k, associated unambiguously to K. Consequently, the hard problem of identifying the p-class tower group G is reduced to an easy computation of low degree arithmetical invariants.
Cite
@article{arxiv.1504.00851,
title = {Periodic sequences of p-class tower groups},
author = {Daniel C. Mayer},
journal= {arXiv preprint arXiv:1504.00851},
year = {2015}
}
Comments
11 pages, 4 figures, will be presented at the International Conference on Groups and Algebras (ICGA), Shanghai, July 2015