TITLE:
Index-p Abelianization Data of p-Class Tower Groups
AUTHORS:
Daniel C. Mayer
KEYWORDS:
p-Class Groups, p-Principalization Types, p-Class Field Towers, Quadratic Fields, Second p-Class Groups, p-Class Tower Groups, Coclass Graphs
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.5,
April
20,
2015
ABSTRACT: Given a fixed prime number p, the multiplet of abelian type
invariants of the p-class groups of
all unramified cyclic degree p extensions of a number field K is
called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable
information for determining the Galois group of the second Hilbert p-class field and the p-capitulation
type of K. For p=3 and a number field K with elementary p-class group of rank
two, all possible IPADs are given in the complete form of several infinite
sequences. Iterated IPADs of second order are used to identify the group of the maximal
unramified pro-p extension of K.