%0 Journal Article %T Index-<i>p</i> Abelianization Data of <i>p</i>-Class Tower Groups %A Daniel C. Mayer %J Advances in Pure Mathematics %P 286-313 %@ 2160-0384 %D 2015 %I Scientific Research Publishing %R 10.4236/apm.2015.55029 %X

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. %K < %K i> %K p< %K /i> %K -Class Groups %K < %K i> %K p< %K /i> %K -Principalization Types %K < %K i> %K p< %K /i> %K -Class Field Towers %K Quadratic Fields %K Second < %K i> %K p< %K /i> %K -Class Groups %K < %K i> %K p< %K /i> %K -Class Tower Groups %K Coclass Graphs %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=55789