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arXiv · 2508.17510

Coclass of the second 3-class group

Siham Aouissi·Daniel C. Mayer
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Abstract

By means of parametrized presentations of finite metabelian 3-groups, it is proved that the coclass cc(M) of the second 3-class group M=Gal(F_3^2(K)/K) of any algebraic number field K with elementary bicyclic 3-class group Cl_3(K)=(3,3) is determined unambiguously by the second largest order ord(Cl_3(E_2))=3^{cc(M)+1} among the four 3-class groups of the unramified cyclic cubic extensions E_i (i=1,..,4) of K. Minimal discriminants of quadratic and cubic fields K with assigned coclass cc(M) are computed from extensive databases of 3-class numbers ord(Cl_3(E_i)) as an application.

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Siham Aouissi, Daniel C. Mayer. 2025-08-24. Coclass of the second 3-class group. https://doi.org/10.1007/s40590-025-00816-7

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