The 3-class groups of Q(3√p) and its normal closure

作者：Li, Jianing; Zhang, Shenxing^*

来源：Mathematische Zeitschrift, 2022, 300(1): 209-215.

DOI：10.1007/s00209-021-02797-5

• Class groups
• Pure cubic fields
• Ambiguous class number formulas

We determine the 3-class groups of Q(3 root p) and K = Q(3 root p, root-3) when p = 4,7 mod 9 is a prime and 3 is a cube modulo p. This confirms a conjecture made by Barrucand-Cohn, and proves the last remaining case of a conjecture of Lemmermeyer on the 3-class group of K.

• 单位
  中国科学院