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Nov
20
comment Finite abelian groups as class groups
@Pete, I can't comment on your answer, but I think you meant to say that the order of the group $2 H_D$ goes to infinity. The order of $H_D/2 H_D$ (as you know) corresponds to the genus field, which has order $2^{d-1}$ where $d$ is the number of prime factors of the discriminant.
Nov
20
awarded  Teacher
Nov
19
answered Finite abelian groups as class groups