TITLE:
Periodic Sequences of p-Class Tower Groups
AUTHORS:
Daniel C. Mayer
KEYWORDS:
p-Class Field Towers, p-Principalization, p-Class Groups, Quadratic Fields, Multiquadratic Fields, Cubic Fields, Finite p-Groups, Parametrized Pc-Presentations, p-Group Generation Algorithm
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.7,
June
30,
2015
ABSTRACT: Recent examples of periodic bifurcations in
descendant trees of finite p-groups with
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
, resp.
. 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.