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 .
Keywords<i>p</i>-Class Groups<i>p</i>-Principalization Types<i>p</i>-Class Field TowersQuadratic FieldsSecond <i>p</i>-Class Groups
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