2021 Volume 53 Pages 1-16
For a fixed integer n ≥ 1, let p = 2nℓ + 1 be a prime number with an odd prime number ℓ and let F = Fp,ℓ be the real abelian field of conductor p and degree ℓ. When n ≤ 21, we show that a prime number r does not divide the class number hF of F whenever r is a primitive root modulo ℓ with the help of computer. This generalizes a result of Jakubec and Metsänkylä for the case n = 1.