Pointwise Bound for ℓ-torsion in Class Groups II: Nilpotent Extensions

2020/06/18 by Wang, Jiuya · 1 citation
#11R29 #20D15 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.10295

Abstract

For every finite p-group G_p that is non-cyclic and non-quaternion and every positive integer ℓ≠ p that is greater than 2, we prove the first non-trivial bound on ℓ-torsion in class group of every G_p-extension. More generally, for every nilpotent group G where every Sylow-p subgroup G_p⊂ G is non-cyclic and non-quaternion, we prove a non-trivial bound on ℓ-torsion in class group of every G-extension for every integer ℓ>1.

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