Principalization algorithm via class group structure
Daniel C. Mayer (2014)
Journal de Théorie des Nombres de Bordeaux
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For an algebraic number field with -class group of type , the structure of the -class groups of the four unramified cyclic cubic extension fields , , of is calculated with the aid of presentations for the metabelian Galois group of the second Hilbert -class field of . In the case of a quadratic base field it is shown that the structure of the -class groups of the four -fields frequently determines the type of principalization of the -class group of in . This...