In this article we classify all imaginary bicyclic biquadratic fields which have an elementary 2-class group provided the discriminant of the real quadratic subfield has no prime divisors congruent to 3 modulo 4. A necessary condition for a biquadratic field to have elementary 2-class group is that no quadratic subfield have a cyclic factor of order greater than 4 in its 2-class group. However, when this condition is satisfied, it is shown that every abelian group of exponent 2 or 4 occurs as a 2-class group of some biquadratic field.

elementary 2-class group, imaginary bicyclic biquadratic fields.