3-class field towers of exact length 3

2013/12/01 by Bush, MIchael R., Mayer, Daniel C. · 1 citation
#11R29 #11R37 (Primary) 11R11 #20D15 #20F14 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1312.0251

Abstract

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 Cl₃(K) ≅ [3,3]. Our results provide the first examples of finite p-class towers of length > 2 for an odd prime p.

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