Let p be a prime. The 2-primary part of the class group of the pure quartic field \({\mathbb {Q}}(\root 4 \of {p})\) has been determined by Parry and Lemmermeyer when \(p \not \equiv \pm \, 1\bmod 16\). In this paper, we improve the known results in the case \(p\equiv \pm \, 1\bmod 16\). In particular, we determine all primes p such that 4 does not divide the class number of \({\mathbb {Q}}(\root 4 \of {p})\).We also conjecture a relation between the class numbers of \({\mathbb {Q}}(\root 4 \of {p})\) and \({\mathbb {Q}}(\sqrt{-2p})\). We show that this conjecture implies a distribution result of the 2-class numbers of \({\mathbb {Q}}(\root 4 \of {p})\).

令p为质数。该类基团的纯四次场的2初级部分\（{\ mathbb {Q}}（\根4 \ {P}）\的）已经由帕里和Lemmermeyer当确定\（P \不\当量\ pm \，1 \ bmod 16 \）。在本文中，我们改进了\（p \ equiv \ pm \，1 \ bmod 16 \）情况下的已知结果。特别是，我们确定所有素数p使得4不除\（{\ mathbb {Q}}（\ root 4 \ of {p}）\）的类号。我们还推测\（{\ mathbb {Q}}（\ root 4 of of {p}）\）和\（{\ mathbb {Q}}（\ sqrt {-2p}）\）。我们证明这个猜想暗示了2类数的分布结果\（{\ mathbb {Q}}（\ root 4 \ of {p}）\）。