DETERMINATION OF ALL NONQUADRATIC IMAGINARY CYCLIC NUMBER-FIELDS OF 2-POWER DEGREES WITH IDEAL CLASS-GROUPS OF EXPONENTS LESS-THAN-OR-EQUAL-TO-2

We determine all nonquadratic imaginary cyclic number fields K of 2-po wer degrees with ideal class groups of exponents less than or equal to 2, i.e., with ideal class groups such that the square of each ideal c lass is the principal class, i.e., such that the ideal class groups ar e isomorphic to some (Z/2Z)(m), m greater than or equal to 0. There ar e 38 such number fields: 33 of them are quartic ones (see Theorem 13), 4 of them are octic ones (see Theorem 12), and 1 of them has degree 1 6 (see Theorem 11).