Article citationsMore>>

Besche, H.U., Eick, B. and O’Brien, E.A. (2005) The Small Groups Library—A Library of Groups of Small Order, 2005, an Accepted and Refereed GAP Package. MAGMA.

has been cited by the following article:

• TITLE: p-Capitulation over Number Fields with p-Class Rank Two

  AUTHORS: Daniel C. Mayer

  KEYWORDS: Hilbert p-Class Field Tower, Maximal Unramified Pro-p Extension, p-Capitulation of Class Groups, Real Quadratic Fields (3, 3)

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.7, July 25, 2016

  ABSTRACT: Theoretical foundations of a new algorithm for determining the p-capitulation type ù(K)of a number field K with p-class rank ?=2 are presented. Since ù(K) alone is insufficient for identifying the second p-class group G=Gal(Fp2K∣K)of K, complementary techniques are deve- loped for finding the nilpotency class and coclass of . An implementation of the complete algorithm in the computational algebra system Magma is employed for calculating the Artin pattern AP(K)=(τ (K),ù(K)) of all 34631 real quadratic fields K=Q(√d)with discriminants 0d8 and 3-class group of type (3, 3). The results admit extensive statistics of the second 3-class groups G=Gal(F32K∣K) and the 3-class field tower groups G=Gal(F3∞K∣K).