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Journal of Undergraduate Research

Keywords

quadratic fields, 2-Skylow class group, isomorphic, C2kC2

College

Physical and Mathematical Sciences

Department

Mathematics

Abstract

We prove that there are infinitely many imaginary quadratic fields with 2-class group isomorphic to C2kC2 for any given positive integer k. This work is based on a related result for cyclic 2-class groups by Dominguez, Miller and Wong, and our proof proceeds similarly. However, we make some improvements in some of the techniques used. In particular, we provide a more general way of introducing congruence conditions into Perelli’s version of the Goldbach conjecture for polynomials.

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