3-Class field towers of exact length 3

JOURNAL OF NUMBER THEORY

卷:147

Article

Bush, Michael R.¹ 

[1] Washington & Lee Univ, Dept Math, Lexington, VA 24450 USA

关键词: p-Class field towers;    Principalization of p-classes;    Quadratic fields;    Transfer map;    Relation rank;    Inversion automorphism;    Schur sigma-groups;    Central series;    Derived series;   

DOI  :  10.1016/j.jnt.2014.08.010

来源: Elsevier

【 摘 要 】

The p-group generation algorithm is used to verify that the Hilbert 3-class field tower has length 3 for certain imaginary quadratic fields K with 3-class group Cla(K) congruent to [3,3]. Our results provide the first examples of finite p-class towers of length > 2 for an odd prime p. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free