Index-\(p\) abelianization data of \(p\)-class tower groups

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) abelianization data). These invariants have proved to be a valuable information for determining the Galois group (G_p^2) of the second Hilbert (p)-class field and the (p)-capitulation type (\varkappa) 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 (G_p^\infty) of the maximal unramified pro-(p) extension of (K).