Pólya groups of Lecacheux quintic fields have 5-rank arbitrarily large with positive density in the parameter s, implying infinite 5-class field towers for a positive proportion of the fields via Golod-Shafarevich.
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Rank of P\'olya Groups in Lecacheux Parametric Family of Quintic Fields
Pólya groups of Lecacheux quintic fields have 5-rank arbitrarily large with positive density in the parameter s, implying infinite 5-class field towers for a positive proportion of the fields via Golod-Shafarevich.