Class numbers of algebraic number fields of Eisenstein type,II

Let K be an algebraic number field, of degree n, with a completely ramifying prime p, and let t be a common divisor of n and $\text{(p ? 1)}\text{2}$. Then it is proved that if K does not contain the unique subfield, of degree t, of the p-th cyclotomic number field, then we have (h_K, n) > 1, where h_K is the class number of K. As applications, we give several results on h_K of such algebraic number fields K.