ABSTRACT. A formula is obtained for the rank of the 2-Sylow subgroup of the ideal class group of imaginary bicyclic biquadratic fields. This formula involves the number of primes that ramify in the field, the ranks of the 2-Sylow subgroups of the ideal class groups of the quadratic subfields and the rank of a Z 2 -matrix determined by Legendre symbols involving pairs of ramified primes. As applications, all subfields with both 2-class and class group Z 2 ðZ 2 are determined. The final results assume the completeness of D. A. Buell's list of imaginary fields with small class numbers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.