关于C_l~n数域的相对整基和单位

Let K be an algebraic number field, k be a subfield of k. E. Artin and A. Frohlich asked and studied this question: when does K/k have a relative integral basis? i. e., when is the ring O_K, integers of K, a free O_k-module? In the case that K is a C_2~2 field, i. e. a bicyclic biquadratic field, this problem was studied in many papers and, finally, solved by L. C. Washington, R. H.