A Group Theoretic Approach to Cyclic Cubic Fields
A Group Theoretic Approach to Cyclic Cubic Fields
Let (kμ)μ=14 be a quartet of cyclic cubic number fields sharing a common conductor c=pqr divisible by exactly three prime(power)s, p,q,r. For those components of the quartet whose 3-class group Cl3(kμ)≃(Z/3Z)2 is elementary bicyclic, the automorphism group M=Gal(F32(kμ)/kμ) of the maximal metabelian unramified 3-extension of kμ is determined by conditions …